wind energy fundamentals & wind measurements
TRANSCRIPT
1
UNIT-I
WIND ENERGY FUNDAMENTALS & WIND MEASUREMENTS
2
1. Introduction
SUBJECT CODE: SME1602
SUBJECT NAME: WIND AND SOLAR ENERGY
The people of energy dependant countries like India are much aware of the
importance of conversion, conservation and development of new energy sources. Today the
Power Engineer are concerned with three “E‟s” namely Energy, Economics and Ecology
(Environment). Thus the power engineer must try to develop systems that produce large
quantities of energy with minimal cost and with low impact on environment. The proper
balance of these 3 “E‟s” is a major technological challenge.
In any energy conversion process, the energy must be conserved as implied by First
Law of Thermodynamics. (For discussion: Einstein Equation) open system, closed system,
isolated system, energy transformation, energy transfer (involves shaft work) machines).
Energy types:
In general, energy is of two types namely,
Transitional energy: Energy in motion and as such can move across system boundary.
Stored energy: Energy that exists as mass, position in a force field etc., These stored forms
can easily be converted into some form of transitional energy. (For discussion: open system,
closed system, isolated system, energy transformation, energy transfer (involves shaft work)
machines).
Energy Classifications:
The energy can be classified into six major groups namely,
1. Mechanical energy – Transitional energy
2. Electrical energy – Transitional energy
3
3. Electromagnetic energy – Transitional energy
4. Chemical energy – Stored energy
5. Nuclear energy – Stored energy
6. Thermal energy – Transitional energy
Thermal energy is the basic form of energy and all the other energy forms can be
completely converted into thermal energy. Thermal energy can be stored as either sensible
heat or latent heat.
Sensible heat storage is accomplished by increase in temperature while the latent heat
storage is an isothermal process associated with change of phase.
Energy Sources:
It has been divided into three categories namely,
1. Conventional or Exhaustible: Fossil fuels such as crude oil, coal and natural gas.
2. Non-conventional or inexhaustible or continuing or renewable sources: solar, wind,
hydroelectric, biomass, biogas, tidal, geothermal and OTEC.
3. Nuclear sources: nuclear fission and nuclear fusion.
Scope Of Wind Energy In India
Wind power is an affordable, efficient and abundant source of domestic electricity.
It's pollution-free and cost-competitive with energy from new coal- and gas-fired power
plants in many regions. The wind industry has been growing rapidly in recent years. The
Ministry of New and Renewable Energy (MNRE) has fixed a target of 10,500 MW between
2007–12, but an additional generation capacity of only about 6,000 MW might be available
for commercial use by 2012.The MNRE has announced a revised estimation of the potential
wind resource in India from 49,130 MW assessed at 50m Hub heights to 102,788 MW
assessed at 80m Hub height. The wind resource at higher Hub heights that are now prevailing
is possibly even more. India has set a target of achieving overall wind energy installed
4
capacity of 27,300 MW by 2017 and 38,500 MW by 2022. As per NOVONOUS estimates,
this creates an US$31.25 billion opportunity in the wind energy market
in India till 2022.
The wind energy market in India has been growing since the last many years. The
total installed capacity of the Indian Wind Energy market is 21136.20 MW. India stands at
the 5th Rank in terms of the total installed wind power capacity just behind China,USA,
Germany and Spain. But the potential is far from being utilized. It is estimated by the Indian
Wind Energy Association that the Wind power potential for all the states of India put together
would be in the order of 1.5 GW. It can sustain the growing needs of electricity of the Indian
consumers in a sustainable way. The wind energy report aims at providing the reader a
detailed view of the industry with the use of analysis frameworks which help in identifying
the political, economical, social and technical factors that determine the scenario of the
market and the market forces prevailing in the industry. The Key challenges faced by existing
players and the barriers for a new player entering into the market, are also covered. It also
identifies the role played by the central and the state governments by analyzing the incentives
and subsidies offered by central and state governments.
It also provides details about risks associated with credit, policy and technical factors
in Indian wind energy market.Detailed company profiles including their position in wind
energy value chain, financial performance analysis, product and service wise business
strategy, SWOT analysis and key customer details for eleven companies namely Suzlon
Energy Limited, Gamesa Wind Turbines Private Limited, Vestas Wind Technology India
Private Limited, Wind World India Limited, Global Wind Power Limited, Inox Wind
Limited, Kenersys India Private Limited, Regen Power tech Private Limited, GE India
Industrial Private Limited, RRB Energy Limited and LM Wind Power Technologies (India)
Pvt. Ltd.
Importance of Energy conservation
The earth provides enough to satisfy every man‟s needs but not every man‟s greed said
Gandhiji. Hard facts on why energy conservation is a must are outlined below.
We use energy faster than it can be produced - Coal, oil and natural gas - the most
utilised sources take thousands of years for formation.
Energy resources are limited - India has approximately 1% of world‟s energy
resources but it has 16% of world population.
5
Most of the energy sources we use cannot be reused and renewed - Non renewable
energy sources constitute 80% of the fuel use. It is said that our energy resources may
last only for another 40 years or so.
We save the country a lot of money when we save energy - About 75 per cent of our
crude oil needs are met from imports which would cost about Rs.1, 50,000 crore a
year
We save our money when we save energy - Imagine your savings if your LPG
cylinder comes for an extra week or there is a cut in your electricity bills
We save our energy when we save energy - When we use fuel wood efficiently, our
fuel wood requirements are lower and so is our drudgery for its collection
Energy saved is energy generated - When we save one unit of energy, it is equivalent
to 2 units of energy produced
Save energy to reduce pollution - Energy production and use account to large
proportion of air pollution and more than 83 percent of greenhouse gas emissions
An old Indian saying describes it this way - The earth, water and the air are not a gift
to us from our parents but a loan from our children. Hence we need to make energy
conservation a habit.
How wind is caused?
Wind is basically caused by the solar energy irradiating the earth. So wind energy is
an indirect manifestation of solar energy. Wind results from air in motion. Air in motion
arises from a pressure gradient. Winds are caused because of two factors namely:
1. the absorption of solar energy on the earth‟s surface and in the atmosphere.
2. the rotation of the earth about its axis and its motion around the sun.
Because of these factors alternate heating and cooling cycles occur, differences in
pressure are created and the air is caused to move.
Wind, being the commercially viable and economically competitive renewable source is
going to play an important role in the future meeting the energy demand.
Global leaders in wind energy generation
untry Installed capacity, MW
Germany 14609
USA 6352
Spain 6202
Denmark 3115
6
Application of wind power: water pumping wind mill.
Advantages:
Its potential as a source of power is reasonably good and its capture produces no
pollution.
Disadvantages:
Energy is available in dilute form.
Availability of the energy varies considerably over a day with seasons. For these
reasons, the face areas of the machines, which extract energy from the wind have to
be necessarily large and a continuous supply of mechanical or electrical power cannot
be obtained from them.
Principle of wind energy conversion: Energy available in the wind is basically the KE of
large masses of air moving over the earth‟s surface. Blades of the wind turbine receive this
KE, which is then transformed to mechanical or electrical forms. The efficiency of converting
wind to other useful energy forms greatly depends on the efficiency with which the rotor
interacts with the wind stream.
India 2120
7
Fundamentals of Wind Energy
1. Wind Energy: Wind is caused by flow of air from high pressure area to low
pressure area and this difference in pressure is result of heating of the uneven
earth's surface by sun. So we can say that wind energy is a form of solar energy.
2. Wind power:Wind power is the conversion of wind energy into a useful form of
energy, such as using wind turbines to make electrical power, windmills for
mechanical power and wind pumps for water pumping.
3. Wind Turbine:A turbine is a rotary mechanical device that extracts energy from
a fluid flow and converts it into useful work. A turbine is a turbo-machine with
at least one moving part called a rotor assembly, which is a shaft with blades
attached. Moving fluid acts on the blades so that they move and impart
rotational energy to the rotor. A wind turbine is a device that converts kinetic
energy from the wind into electrical power.
1. Foundation: Its the basement of a wind turbine on which the whole self weight
of wind turbine's will come. It is normally under the surface and it cannot be
seen.
2. To Electric Grid: This is the connection from which the generated power is sent
to electric grid with the help of electric wires.
8
3. Tower: It is the supporting structure for nacelle and rotor. The nacelle is placed
above this tower. Tower is a assembly of number of cylindrical hallow structure
which are assembled at the site (wind farm).
4. Access Ladder: There will be a ladder inside the tower from basement to the
top so that one can get access to the nacelle for any kind of repair or inspection
work.
5. Yaw Control: Since the direction of wind keeps on changing with respect to
time and the rotor should be placed in the direction of wind to get the maxim
power output, this yaw control helps in o changing the direction of the rotor and
will place it in the direction of the wind.
6. Nacelle: It is a rectangle like structure that contains generator, controller
system, cooler etc. When yaw controls activates the whole nacelle is rotated in
the direction of wind.
7. Generator: It is the unit responsible for power generation.
8. Anemometer: It is a device that is used for wind speed measurement. This data
is sent to control system.
9. Brake: It is used to stop the rotor that is rotating. Usually brakes are applied
when weather conditions are not good to generate power or the rpm of the rotor
is above normal speed which may not suite to generator.
10. Gear Box: It consist of gears that increases the rpm of the rotor to suite to the
rpm of generator.
11. Rotor Blade: Blades are the rotating member of wind turbine that makes the
shaft to rotate which is connected to gearbox and then to generator. Blades are
of aerofoil shape and length will vary from 30 m to 80m (approx.) depending
on the rated power of wind turbine.
12. Pitch Control: It is used to change the angle of inclination, pitch angle which
are responsible for getting maximum efficiency.
13. Rotor Hub: It is the one which holds the rotor blade and it will also rotate along
with blades.
Site Selection
Anemometers are small and simple devices. A number of the newer units are
9
digital hand held recorders which allow you to easily check wind conditions in
different parts of your property. The anemometers aren't hard to set up and many can
record not only wind speed but temperature and humidity as well. If your schedule
allows you may wish to take recordings at different times of the year in order to get a
complete picture of how the wind changes at your location by season.
Another major consideration when selecting a site is the proximity of the wind
tower to your home or business. In most cases you don't want the wind tower attached
to the building itself because of both noise and structural vibration considerations.
However, if the tower is too far away then you could incur significant costs in running
a power line from the tower to your house where the electric meter is or, if you are off
the grid, to where your batteries are stored. That tower on the hill may sound nice but if
the hill is two miles away you might find that it will cost you more to run the line then
to have put up the tower in the first place.
Terrain is another consideration. If we live in a hilly area it is good to take
advantage of hills in order to gain additional height for your tower. In particular, take
care to avoid locations where you are on the leeward (sheltered) side of a hill since it
would cut off the wind. Don't just consider existing obstacles. If you are putting up the
tower prior to building a residence, consider the impact the home itself will have on
wind patterns. Also take into consideration any locations where you may be planning
to put up trees which could block the wind.
The impact even a small reduction in wind velocity will have on your ability to
generate power. Wind power increases exponentially relative to speed (V3). A site with
an annual average wind speed of about 12.6 miles per hour (5.6 meters per second), has
twice the energy available as a site with a 10 mile per hour (4.5 meter per second)
average.
Even if have to be a perfect site for wind power, you should always check state
and local regulations before investing money in a wind energy solution. Take the time
to research local zoning requirements. Many communities have put up strong
restrictions on the height of structures. Wind turbines perform better the higher they are
placed but you may find that a 75 or 100 foot tower may violate local zoning
10
requirements. For more information on the impact of regulations check out the
Government Regulations section on our menu.
Also be considerate of our neighbors, particularly if they live close to where
you are thinking of placing your wind tower. People can get awfully fussy about
having their views block and what might seem like a trivial view to you may be a very
big issue for them. Talk to your neighbors before proceeding, and if there is a local
community group for your housing area make sure you get their input as well. Your
neighbors might object to a wind machine that blocks their view, or they might be
concerned about noise.
UNIT-II
WIND MACHINES
WINDMACHINES
SUBJECT CODE: SME1602
SUBJECT NAME: WIND AND SOLAR ENERGY
Classification of wind machines:
Wind energy is an indirect source of solar energy conversion and can be utilized to run wind
mill, which in turn drives a generator to produce electricity.
Wind machines are generally classified in terms of the orientation of the axis of rotation of
their rotors as horizontal axis machines & vertical axis machines.
In a horizontal axis machine, the rotor axis is horizontal and is continuously adjusted in a
horizontal plane so that it is parallel to the direction of the wind stream. These machines have
to face the direction of the wind in order to generate power. Eg: - Multi blade type, Propeller
type & Sail type wind mills.
Multi blade type Propeller type Sail type
In a vertical axis machine, the rotor axis is vertical and fixed, and it is r to both the surface
of the earth and the wind stream. These machines run independently of the direction of the
wind because they rotate about a vertical axis. Eg:- Savonius type & Darrieus type wind
mills(Designed in 1920 and patented in 1931).
Savonius type Darrieus type
Lift Force and Drag Force:
o The extraction of power and hence energy from the wind depends on creating certain
forces and applying them to rotate or to translate a mechanism.
o There are two primary mechanisms for producing forces from the wind namely lift
force and drag force.
o Lift force act perpendicular to the air flow while drag force act parallel to the
direction of air flow.
o Lift force is produced by changing the velocity of the air stream flowing over either
side of the lifting surface (aerofoil): speeding up of the air flow causes the pressure to
drop while slowing the air flow down leads to increase in pressure.
o In other words, any change in velocity generates a pressure difference across the
lifting surface. This pressure difference produces a force that begins to act on a high
pressure side and moves towards the low pressure side of the aerofoil.
o A good aerofoil should have more lift/drag ratio. For efficient operation, a wind
turbine blade needs to function with as much lift and as little drag as possible because
the drag force dissipates the energy..
o The design of each wind turbine blade specifies the angle at which the air foil should
be set to achieve the maximum lift to drag ratio. Wind speeds for a wind machine:
Cut-in Speed: It is the wind speed below which the machine does not rotate and no power is
produced.
Design Speed: It is the wind speed at which the machine produces its rated output. Usually
the output is held constant at the rated value for wind speeds greater than the design speed.
This is achieved by some form of governing mechanism.
Cut-out Speed: It is the wind speed at which it is advisable to shut down the wind machine in
order to avoid mechanical damage.
Performance Calculations:
Power available in the wind stream =
1 AV 3
----- Eqn. 1
2
The equation implies that the factors influencing the power available in the wind
stream are air density, area of the wind rotor and the wind velocity. Effect of wind
velocity is more prominent as shown. The density of air decreases with the increase in
site elevation and temperature. The air density may be taken as 1.225 for most of the
practical cases. Due to this relatively low density, wind is rather a diffused source of
energy. Hence large sized systems are often required for substantial power
production.
The prominent factor deciding the power available in the wind is its velocity. When
the wind velocity is doubled, the available power increases by 8 times. In other words,
for the same power, rotor area can be reduced by a factor of 8, if the system is placed
at a site with double the wind velocity. Hence selecting the right site play a vital role
in the success of a wind power projects.
A = swept frontal area of the machine; V = Free stream wind speed.
Wind turbine power and torque:
Theoretical power available in the wind stream is given by eqn. 1. However, a turbine
cannot extract this power completely from the wind. When the wind stream passes the
turbine, a part of its KE is transferred to the rotor and the air leaving the turbine carries the
rest away. Actual power produced by a rotor would thus be decided by the efficiency with
which this energy transfer from the wind to the rotor takes place. This efficiency is usually
termed as the power coefficient. Thus, the power coefficient of the rotor can be defined as the
ratio of actual power developed by the rotor to the theoretical power available in the wind.
1. Power Coefficient, Cp 1
; Pe 3 Power extracted by the rotor
2 AV
C p or ideal or maximum theoretical efficiency, max powerextractedbytherotor
poweravailableint hewindstream
The power coefficient of a turbine depends on profile of the rotor blades, blade arrangement
and setting etc., These parameters should be at its optimum so as to attain maximum C p at a
wide range of wind velocities.
2. Lift Coefficient = CL 1
; Ab 2
Projected area of the blade facing the wind.
2
C Liftforceo ntheblade
AbV
;
F , Lift Force is r to the direction of the incoming air
L Forceofthefreestreamwind L
flow and arises due to the unequal pressure on the two surfaces of the blade.
Pe
FL
3. Drag Coefficient = CD 1
; FD , Drag Force is parallel to the direction of the 2
2 AbV
incoming air flow and arises due to the viscous friction forces at the surface of the blade as
well as the unequal pressure on the blade surfaces.
4. Tip speed ratio,
Speedofthebla det ip
Freestreamwindspeed R
V
; = angular velocity of the rotor
and R = tip radius
This definition holds good for a horizontal axis wind machine. Blade should have high tip
speed ratio.
For a vertical axis m/c, PeripheralSpeedatthemiddleofthebladelength
Freestreamofthewindspeed
5. Solidity of a wind m/c, BladeArea
SweptFrontalArea( facearea)ofthemachine =
Nc
R
(This
definition holds good for a horizontal axis machine). Blades should have low solidity.
For a vertical axis machine:-
Nc
..for Darrieus type and R
Nc
2R
...for other types
FD
c
c
N = No. of blades; R = mean radius & c =
mean chord of the blades
P 8 AV 3
16 1 AV 3
6. Maximum Power, max 27 g i . i
c
1 AV 3
27 2 gc
P 0.593i = 0.593 P
max
2
gc total
0.593 is known as the Betz Coefficient. C p cannot exceed 0.593 for a horizontal axis m/c.
max
Pm ax
Ptotal
0.593 16
27
Forces on the blades & Thrust on the turbines for propeller type wind machines: There are 2
types forces are acting on the blades namely,
1. The circumferential force or torque acting in the direction of wheel rotation.
2. The axial force acting in the direction of wind stream.
The torque T can be obtained from T = P
P
DN
in Newton;
4
N = wheel revolution per unit time, (1/S); D = diameter of the turbine wheel = √
.A (in
meters); angular velocity of the turbine wheel in m/s.
P
1 AV 3 Actual efficiency, = P = . P
total = . i P
total 2 gc
1 AV 3 1 DV 3 16 Torque, T = i i . At maximum efficiency, , the
2gc DN 8gc N 2 DV 3
max
27
torque has maximum value of Tmax which is equal to: T i . max 27g N
g = gravitational conversion constant = 1 (kg m / s2) / N
The axial force or thrust is given by the equation:
F 1 A(V 2 V 2 )
D 2 (V 2 V 2 ) .
x 2g i e
8g i e
c c
The above equation implies that the axial forces are proportional to the square of the diameter of the
turbine wheel. This limits the turbine wheel diameter of the large size.
Power Density:
The power density is the K.E flowing per unit area and is given by
Power Density = Power
1 V V 2
1 V 3 ;
Area 2 2
air density in Kg / m3 and V = wind speed in m / s.
Ideal power required to pump the water = gQH watts
= density of water; g = acceleration due to gravity; Q = discharge; H = differential head.
Expression for the maximum power developed by a horizontal axis wind machine.
The wheel thickness of a horizontal axis wind machine is assumed to be ab.
Let pi and vi are the wind pressure and velocity at the upstream of the turbine.
pe and ve are the wind pressure and velocity at the downstream of the turbine.
ve is less than vi because kinetic energy is extracted by the turbine.
v v
v v
a b i e
c
i
e
Considering the incoming air between i and a as a thermodynamic system and assuming the
air density remains constant (since changes in p and T are very small compared to ambient),
that the potential energy is zero and no heat or work is added or removed between i and a, the
general energy equation reduces to the kinetic and flow energy terms only. Thus,
v2 v2
For inlet: p v i p v a ..........................1.a i 2g a 2g
2
p i p 2gc
2
a .................... 1.b 2gc
Similarly for exit:
2
p e p 2gc
2
b ...................... 2
2gc
The wind velocity across the turbine decreases from a to b since kinetic energy is converted
to mechanical work there. The incoming velocity vi does not decrease abruptly but gradually
as it approaches the turbine to va and as it leaves it to ve . Thus vi > va and vb > ve and
therefore from equations 1 and 2: we have pa > pi and pb < pe ; that is, the wind
pressure rises as it approaches, then as it leaves the wheel..
Combining equations 1 and 2, we get
v2 v2 v2 v2 p p p i a p e b 3
2gc 2gc
It can be assumed that wind pressure at e can be assumed to be ambient,
i.e., pe pi .......................... 4
As the blade width a.b is very small as compared to total distance considered, it can be
assumed that velocity within the turbine does not change much and therefore
va vt vb........................................ 5
Combining equations 3 to 5 gives,
pa v 2 v 2
p i e 6
2gc
The axial force Fx in the direction of wind stream on a turbine wheel with the projected area
perpendicular to the stream is given by
b
c
a
b
v e
c
v2 v2
Fx pa pbA A
i
2gc
e 7
This force is also equal to change in momentum of the wind (from Newton‟s II law), hence
.
Fx (mv) / gc
.
where m = mass flow rate = Avt
Thus Fx c
Avt vi ve………………….8
Equating equations 7 and 8
v2 v2 1
A
i
2gc
e =
Avt vi ve and therefore gc
v 1 v
t 2
i ve …………………………9
Considering the total thermodynamic system bounded by i and e, there is no changes in
potential energy, the internal energy is there from Ti and Te , and flow energy is there from
pi v and pe v . In the system, no heat is added or rejected, i.e., adiabatic flow.
The general equation now reduces to the steady flow work W and kinetic energy terms,
v2 v2 W = kE kE i e ........................ 10
i e 2g
The power P is defined as the rate of work, and from mass flow rate equation
v2 v2 1
P = m i e
2gc
= 2gc
Avt i 2 ……..11
Combining this with equation 9, we get
P 1
Av v (v 2 v 2 )
4gc i e i e
P 1 Av v v v (v v ) =
A v 2 v 2 2v v v v 4gc
i e i e i e 4g
i e i e i e
= A v3 v 2v
v v 2 v3 2v 2v 2v v 2
4gc i e i e e i e i e
= A v3 v 2v v v 2 v3 12
4gc i e i e e
2 v
1
g
c
i
i
It can be seen from equation 12, where ve is positive in one term and negative in other, that
too low or too high a value for ve results in reduced power. There, thus is an optimum exit
velocity ve opt, thus results in maximum power Pm ax , which can be obtained by
differentiating P, and equating the derivative to zero.
i.e.,
or
d p
dve
d p
= 0
= 3v 2 2v v v 2 0
dve e i e i
The above equation is solved for a positive ve to give ve opt. The above quadratic has two
solutions, i.e., v = v and v = 1
v , only second solution is physically acceptable. Thus,
e i e 3
i
v opt = 1
v ................................................. 13
e 3
i
Using eqn.13 in eqn.12, for an ideal horizontal axis wind machine, we get
P 8
Av 3 .....................................
14
max 27 g
i
P 16
1 Av 3 1 Av3
= 0.593 i = 0.593 P
max
27 gc 2 2 gc total
Pm ax = 0.593 Ptotal
Wind is basically caused by the solar energy irradiating the earth. So wind energy is an
indirect manifestation of solar energy. Wind results from air in motion. Air in motion arises
from a pressure gradient. Winds are caused because of two factors namely:
1. the absorption of solar energy on the earth‟s surface and in the atmosphere.
2. the rotation of the earth about its axis and its motion around the sun.
Because of these factors alternate heating and cooling cycles occur, differences in pressure
are created and the air is caused to move.
Advantages:
Its potential as a source of power is reasonably good and its capture produces no pollution.
c
i
Disadvantages:
1.Energy is available in dilute form. 2. Availability of the energy varies considerably over a
day with seasons. For these reasons, the face areas of the machines, which extract energy
from the wind have to be necessarily large and a continuous supply of mechanical or
electrical power cannot be obtained from them.
Classification of wind machines:
Wind energy is an indirect source of solar energy conversion can be utilized to run wind mill,
which in turn drives a generator to produce electricity. Wind machines are generally
classified in terms of the orientation of the axis of rotation of their rotors as horizontal axis
machines & vertical axis machines.
In a horizontal axis machine, the rotor axis is horizontal and is continuously adjusted in a
horizontal plane so that it is parallel to the direction of the wind stream. These machines have
to face the direction of the wind in order to generate power. Eg: - Multi blade type, Propeller
type & Sail type wind mills.
In a vertical axis machine, the rotor axis is vertical and fixed, and it is r to both the surface
of the earth and the wind stream. These machines run independently of the direction of the
wind because they rotate about a vertical axis. Eg:- Savonius type & Darrieus type wind
mills.
Performance Calculations:
1. Power Coefficient, Cp 1
; Pe 3
Power extracted by the rotor
2 AV
C p or ideal or maximum theoretical efficiency, max powerextractedbytherotor
poweravailableint hewindstream
A = swept frontal area of the machine; V = Free stream wind speed.
2. Lift Coefficient = CL 1
; Ab 2
Projected area of the blade facing the wind.
2
C Liftforceo ntheblade
AbV
;
F , Lift Force is r to the direction of the incoming air
L Forceofthefreestreamwind L
flow and arises due to the unequal pressure on the two surfaces of the blade.
Pe
FL
3. Drag Coefficient = CD 1
; FD , Drag Force is parallel to the direction of the 2
2 AbV
incoming air flow and arises due to the viscous friction forces at the surface of the blade as
well as the unequal pressure on the blade surfaces.
4. Tip speed ratio, Speedofthebla det ip
Freestreamwindspeed R
V
; = angular velocity of the rotor
and R = tip radius
This definition holds good for a horizontal axis wind machine.
For a vertical axis m/c, PeripheralSpeedatthemiddleofthebladelength
Freestreamofthewindspeed
5. Solidity of a wind m/c, BladeArea
SweptFrontalArea( facearea)ofthemachine =
Nc
R
(This
definition holds good for a horizontal axis machine).
For a vertical axis machine:- Nc
..for Darrieus type and R
Nc
2R
...for other types
N = No. of blades; R = mean radius & c = mean chord of the blades
P 8 AV 3 16 1 AV 3 6. Maximum Power, max 27 g
i . i c
1 AV 3
27gc 2 gc
P 0.593i = 0.593 P max
2
gc total
0.593 is known as the Betz Coefficient. C p cannot exceed 0.593 for a horizontal axis m/c.
max
Pm ax
Ptotal
0.593 16
27
Forces on the blades and Thrust on the turbines for propeller type wind machines:
There are 2 types forces are acting on the blades namely,
1. The circumferential force or torque acting in the direction of wheel rotation.
2. The axial force acting in the direction of wind stream.
The torque T can be obtained from T = P
P
DN
in Newton;
FD
c
c
4 N = wheel revolution per unit time, (1/S); D = diameter of the turbine wheel = √
.A (in
meters); angular velocity of the turbine wheel in m/s.
P
1 AV 3 Actual efficiency, = P = . P
total = . i P
total 2 gc
1 AV 3 1 DV 3 16 Torque, T = i i . At maximum efficiency, , the
2gc DN 8gc N 2 DV 3
max
27
torque has maximum value of Tmax which is equal to: T i . max 27g N
The axial force or thrust is given by the equation:
F 1 A(V 2 V 2 )
D 2 (V 2 V 2 ) .
x 2g i e
8g i e
The axial force on a turbine wheel operating at maximum efficiency is given by
F D 2V 2 ; where
V Velocity at the upstream of the turbine.
x max 9g i i
Ve Velocity at the downstream of the turbine.
The above equation implies that the axial forces are proportional to the square of the diameter
of the turbine wheel. This limits the turbine wheel diameter of the large size.
Some more formulae: 1. The power density (i.e., the power per unit area normal to the
wind) is the K.E flowing per unit area and is given by
Power Density =
Power
1 V V 2
1 V 3 ; air density and V = wind speed
Area 2 2
2. Ideal power required to pump the water =
gQH watt
c c
1
UNIT 3
SOLAR RADIATION AND COLLECTORS
2
SOLAR RADIATION AND COLLECTORS
SUBJECT CODE SME1602
SUBJECT NAME WIND AND SOLAR ENERGY
Solar geometry :
Solstice: Either of the two occasions in a year when the sun is directly above either the
furthest point north or the furthest point south on the equator that it ever reaches. These are
the times in the year in the middle of summer or winter, when there are the longest hours of
the day or night (summer solstice [longest day] / winter solstice [longest night]).
Equinox: Either of the two occasions in a year, when the day and night are of equal length
and the sun is directly above the equator.
Equator: Equator is an imaginary line on the Earth's surface equidistant from the North Pole
and South Pole that divides the Earth into a Northern Hemisphere and a Southern
Hemisphere. The latitude of the Equator is 0°.
Longitude (λ):- It is a geographic coordinate that specifies the east-west position of a point
on the Earth's surface. It is an angular measurement, usually expressed in degrees, minutes
and seconds, and denoted by the Greek letter lambda (λ). The longitude of Mumbai is 72˚51‟.
Latitude ( ):-The latitude of a location on the Earth is the angular distance of that location
south or north of the equator. The latitude is usually measured in degrees. The equator has a
latitude of 0°, the North pole has a latitude of 90° north (written 90° N or +90°), and the
South pole has a latitude of 90° south (written 90° S or −90°). Together, latitude and
longitude can be used as a geographic coordinate system to specify any location on the globe.
For example, the Eiffel Tower has latitude of 48° 51′ 29″ N-- that is, 48 degrees plus 51
minutes plus 29 seconds. Alternatively, latitude may be measured entirely in degrees, e.g.
48.8583° N.
Diurnal: - Specialized happening over the period of the day or being active or happening
during the day rather than at night.
Zenith: - It is a point on the celestial sphere directly over the head. It would change with
respect to the location.
Nadir: - It is a point on the celestial sphere diametrically opposite to the zenith. This would
3
also change w.r.to the location. Unlike zenith, nadir is not visible.
Celestial sphere: - The sky may conveniently be assumed to be a large sphere and this
imaginary sphere is called celestial sphere.
Note that the Zenith is opposite the Nadir.
Meridian:- Some reference location on the earth will aid in locating a particular position.
The location of Royal Observatory, Greenwich in southeast London has been universally
accepted as a reference point. Prime Meridian passes through this observatory is known as
the International Meridian or Greenwich Meridian. The meridian is the outer orange
circle which Z, the zenith, lies on. O is the observer.
In the sky, a meridian is an imaginary great circle on the celestial sphere. It passes through
the north point on the horizon, through the celestial pole, up to the zenith, through the south
point on the horizon, and through the nadir, and is perpendicular to the local horizon. [ante
meridiem (a.m., "before midday") and post meridiem (p.m., English: "after midday")]
Solar Constant ( Gsc ): This is the amount of energy received in a unit time on unit area
perpendicular to the sun‟s direction at the mean distance of the earth from the sun. Its
currently accepted value is 1367 W/m2, though other values, 1353 W/m2, 1367 W/m2 are also
found in the literature.
4
The intensity of extra terrestrial solar flux (ET – outside the earth‟s atmosphere) on
any day of the year (G) measured on the plane normal to radiation would be somewhat
different from G as actual sun-earth distance varies during the year.
Thus, Gon Gsc 1 0.033 cos360 n / 365
Where n is the number of the day of the year. For e.g. n = 1 for January 1 and n = 32 for
February 1. Sun’s radius = 696,342 km with an uncertainty of only 65 km. (from the
report on March 22, 2012, The Hindu)
Solar Declination angle ( ): The earth-sun vector moves in an ecliptic plane. The angle b/w
the earth-sun vector and the equatorial plane is called the solar declination angle. varies
from - 23.45 on December 21 (winter solstice) to + 23.45 on June 21 (summer solstice). It
is zero on the two equinox days of March 21 and September 22.
can be calculated using the relation
δ ( in degrees) = 23.45 sin
360 (284 n)
where n = no. of the day.
365
Solar azimuth angle ( s ), Solar altitude angle ( a ), Solar zenith angle ( z ):
The sun‟s position is usually specified in terms of solar azimuth angle and solar
altitude angle.
The solar altitude angle ( a ) measures sun‟s angular distance from the horizon.
The solar azimuth angle ( s ) measures the sun‟s angular distance in the horizontal
plane from the south. ( s ) is + ve to the east of south and – ve to the west of south.
Solar zenith angle ( z ) is the sun‟s angular distance from the zenith. Thus a and z
are complimentary angles. i.e., a + z = 90.
5
Local Solar Time (LST) or Local Apparent Time (LAT) and standard time:
The rotation of the earth about its axis causes the day and night cycle and is also
responsible for the apparent diurnal motion of the sun.
Solar time is based on the apparent angular motion of the sun across the sky.
Solar noon is the time when the sun crosses the local meridian.
Solar day is defined as the time interval between two successive occasions when the
sun crosses the local meridian. The solar day varies in length throughout the year.
Because of the earth‟s forward movement in its orbit, during this time interval the
time required for one full rotation of the earth is less than a solar day by about 4
minutes.
Hence the standard time (which is a uniform time and is observed from a clock) and
solar time differ.
The time used for calculating the hour angle is the local solar time or local apparent
time. This can be obtained from the standard time observed on a clock by applying
two corrections:
1. The first correction arises because of the difference between the longitude
of the location and the meridian on which the standard time is based. The correction
has a magnitude of 4 minutes for every degree difference in longitude.
2. The second correction called the equation of time correction is due to the
fact that the earth‟s orbit and rate of rotation are subject to small variations. This
correction is based on experimental observations and is plotted in the graph.
Solar time is related to standard time by the following relation,
LAT = Standard time 4 (standard time longitude – longitude of
location) + Equation of time correction.
The – ve sign in the first correction is applicable for the eastern hemisphere, while the
positive sign is applicable for the western hemisphere.
In India, standard time is based on 82.5˚ E.
The Equation of time correction E (in minutes) can also be calculated from the
following empirical relation:
E = 229.18 (0.000075 + 0.001868 cos B – 0.032077 sin B – 0.014615 cos 2B –
0.04089 sin 2B)
6
where, B = (n -1) 360 / 365 and n is the day of the year.
Solar hour angle ( ):- It is an angular measure of time and is equivalent to 15˚ per hour. It
is used extensively to express solar time as it is directly related to the sun‟s position in the
sky. It varies from - 180˚ to + 180˚. Solar hour angle is measured from noon based on LAT.
is positive before solar noon (in the morning) and negative after solar noon (in the
afternoon). For e.g. For 8 a.m. solar time, = +60˚ & for 5 p.m. solar time, = -75˚.
Monthly Average Daily Diffuse Radiation:
Either of the two equations or both can be used for India to calculate the Monthly Average
Daily Diffuse Radiation.
Hd 1.411 1.696 H g
H g Ho
by Modi and Sukhatme
7
o
H
c
s
g
Hd 0.8677 H
S 0.7365
S
by Garg and Garg
g max
Hg K
Ho
Monthly Average Clearness Index
Monthly Average Hourly Global Radiation:
I g
Hg
o a b cos/ f c .................................. by Gueymard
Ho
Where: a = 0.409 + 0.5016 sin ( s - 60˚ )
b = 0.6609 – 0.4767 sin ( s - 60˚ )
Normalizing factor,
s
f a 0.5b 180
sin s
cos
sin
s s cos 180
s
I Monthly Average of the hourly global radiation on a horizontal surface (kJ / m2-h)
I Monthly Average of the ET radiation on a horizontal surface (kJ / m2-h)
Note: Wherever needed, an hourly value (kJ / m2-h) can be calculated from an instantaneous
value by taking the instantaneous value (kW / m2) at the mid-point of the hour and
multiplying by 3600.
Monthly Average Hourly Diffuse Radiation:
I d Io
Hd Ho
………. by Liu and Jordan
Id (a bcos) I0
Hd H 0
……….by Satyamurthy and Lahiri
H
Where: a 0.4922 0.27 /(H / H ) for 0.1 d 0.7
d g g
H
T
I
8
H
or a 0.76 0.113/(H / H )for 0.7 d 0.9
d g g
9
b 2(1 a)(sin s s coss ) /(s 0.5sin 2s )
Solar Radiation on Tilted Surfaces:
Most solar equipment like flat-plate collector, for absorbing solar radiation, is tilted at
an angle to the horizontal. It therefore becomes necessary to calculate the flux which falls on
a tilted surface. This flux is the sum of the beam and diffuse radiation falling directly on the
surface and the radiation reflected onto the surface from the surroundings.
Beam Radiation
Beam radiation flux falling on a tilted surface (cos θ)
cos θ = sin δ sin (φ – β) + cos δ cos ω cos (φ – β)
Beam radiation flux falling on a horizontal surface (cos θz)
cos θz = sin φ sin δ + cos φ cos δ cos ω
Hence tilt factor for beam radiation, rb is given as
rb = cos
cos z
sin sin( ) cos cos cos( )
sin sin cos cos cos
Valid only for a tilted
surface with 0 º
Diffuse Radiation
rd (1 cos ) / 2 valid for any tilted surface with a slope and
(1 cos ) / 2 is the radiation shape factor for a tilted surface w.r.to the sky.
Reflected Radiation
rr (1 cos ) / 2 valid for any tilted surface with a slope and
(1 cos ) / 2 is the radiation shape factor for a tilted surface w.r.to the surrounding ground
and (is the diffuse reflectivity) = 0.2, for concrete or grass surface.
Flux on Tilted Surface:
The flux IT falling on a tilted surface at any instant is given by
IT Ib rb Id rd (Ib Id )rr
10
T
I
H
I I
I
I I
H H
s
H
H H
To calculate hourly radiation falling on a tilted surface for the value of taken at the
mid-point of the hour:
T 1
rb
rd rr
g g g
To calculate monthly average hourly value I if the calculations are done for the
representative day of the month:
T d d 1 r r r
b d r
g g g
Where rb rb on the representative day
rd rd and rr rr
To calculate the daily radiation falling on a tilted surface:
T 1
Rb
Rd Rr
g g g
For a south facing surface ( = 0º ),
R st sin sin( ) cos sin st cos( )
b sin sin cos cos sin
Rd rd and Rr rr
st and s are the sunrise or sunset hour angles (in radians) for the tilted surface and a
horizontal surface respectively.
To calculate monthly average daily radiation falling on a tilted surface if the values are
calculated for the representative day of the month:
T d d 1 R R R
b d r
g g g
Where
Rb Rb on the representative day
Rd Rd and
Rr Rr
Id
Hd
I Id
I
I
I
H Hd
H
s
H
H
11
Terrestrial Radiation: - Long-wave electromagnetic radiation origination from earth & its
atmosphere. It is the radiation emitted by naturally radioactive materials on earth including
uranium, thorium and radon.
Extraterrestrial Radiation: - Electromagnetic radiation which originates outside the earth or
its atmosphere, as in the sun or stars.
Solar Radiation at the Earth’s Surface:-
Solar radiation is received at the earth‟s surface in an attenuated form (reduced in
strength) because it is subjected to the mechanisms of absorption and scattering as it passes
through the earth‟s atmosphere.
Mechanism of absorption:- It occurs primarily because of the presence of ozone and water
vapor in the atmosphere, and to a lesser extent due to other gases like CO2, NO2, CO, O2,
CH4 and particulate matter(- are tiny subdivisions of solid matter suspended in a gas).
Absorption results in an increase in the internal energy of the atmosphere.
Mechanism of scattering: - It occurs due to all gaseous molecules as well as particulate
matter in the atmosphere. This scattered radiation is redistributed in all directions, some
going back into space and some reaching the earth‟s atmosphere.
Solar radiation received at the earth‟s surface are of two types namely beam (or
direct) and diffuse radiation.
Beam or Direct Radiation: - The radiation received at the earth‟s surface without change of
direction, i.e., in line with the sun is called beam or direct radiation. Instrument used:
Pyrheliometer.
Diffuse Radiation: - The radiation received at the earth‟s surface after its direction has been
changed by scattering and reflection is called diffuse radiation.
Instrument used: Pyranometer using shading ring arrangement.
Total Radiation: - The sum of the beam and diffuse radiation is called as total or global
radiation.
Instrument used:- Pyranometer.
Thermopile: - A thermopile is an electronic device that converts thermal energy into
electrical energy. It is composed of several thermocouples connected usually in series or, less
12
commonly, in parallel. Thermopiles do not respond to absolute temperature, but generate an
output voltage proportional to a local temperature difference or temperature gradient. The
output of a thermopile is usually in the range of tens or hundreds of millivolts.
Working Principle of Pyrheliometer: -
A pyrheliometer is an instrument for direct measurement of solar irradiance. Sunlight
enters the instrument through a window and is directed onto a thermopile which converts heat
to an electrical signal that can be recorded. The signal voltage is converted via a formula to
measure watts per square meter. It is used with a solar tracking system to keep the instrument
aimed at the sun. ("Irradiance" is used when the electromagnetic radiation is incident on the
surface).
A pyrheliometer is an instrument which measures beam radiation falling on a surface
normal to the sun‟s rays. In contrast to a pyranometer, the black absorber plate (with the hot
junctions of the thermopile attached to it) is located at the base of the collimating tube. The
tube is aligned with the direction of the sun‟s rays with the help of a two-axis tracking
mechanism and an alignment indicator. Thus the black plate receives only beam radiation
and a small amount of diffuse radiation falling with the „acceptance angle‟ of the instrument.
Pyrheliometer on a solar tracker which keeps the instrument pointed at the sun.
Working principle of Pyranometer to measure global or total radiation:
13
14
It consists of a „black‟ surface which heats up when exposed to solar radiation. Its
temperature increases until the rate of heat gain by solar radiation equals the rate of heat loss
by convection, conduction and reradiation. The hot junctions of a thermopile are attached to a
black surface, while the cold junctions are located under a guard plate so that they do not
receive the radiation directly. As a result, an emf is generated. This emf which is usually in
the range of 0 to 10 mV can be read, recorded or integrated over a period of time and is a
measure of solar radiation.
The pyranometer shown is used commonly in India. It has its hot junction arranged in
the form of a horizontal circular disc of diameter 25 mm and coated with a special lacquer
having a high absorptivity in the solar wavelength region. The disc is placed on a large
diameter guard plate which may be horizontal or sloping. Two concentric hemispheres 30 and
50 mm in diameter respectively, made of optical glass having excellent transmission
characteristics are used to protect the disc surface from the weather. An accuracy of 2 %
can be obtained with the instrument.
Pyranometer to measure diffuse radiation using shading ring: -
This is done by mounting the pyranometer at the centre of a semicircular shading ring.
The shading ring is fixed in such a way that its plane is parallel to the plane of the path of the
sun‟s daily movement across the sky and it shades the thermopile element and the two glass
domes of the pyranometer at all times from direct sunshine. Consequently, the pyranometer
only the diffuse radiation received from the sky.
Shading ring:-
1. ABCD is a horizontal rectangular frame 35 cm x 80 cm with its long sides in an E-
W direction.
2. Two angle-iron arms EF and GH, 70 cm long, are with slots along their length. The
angle-iron arms are pivoted to the sides AB and CD respectively.
3. The arms are pivoted about a horizontal axis which passes through the center of the
rectangular frame and can be adjusted at an angle to the horizontal equal to the latitude of the
station.
4. The movement of the ring up and down the arms allows for changes in the sun‟s
declination..
5. EF and GH carry sliders, SS, on which the semicircular shading ring R is mounted.
The shading ring R is made of Al, 50 mm width, and is bent to a radius of 450 mm. The
15
inner surface of the ring is painted dull black, while the rest of the shading ring is painted dull
matt white. A thick metal plate P is fixed to the bottom of the frame ABCD. This plate P has
16
a circular slot so that the frame when fixed on a masonry platform with nuts and bolts can be
adjusted in its proper position by rotation about a vertical axis. Another thick metal plate P‟ is
fitted to the top of the frame, on which the pyranometer is fitted.
Sunshine recorder: -
The duration of the bright sunshine in a day is measured by means of a sunshine
recorder. The sun‟s rays are focused by a glass sphere to a point on a card strip held in a
groove in a spherical bowl mounted concentrically with the sphere. Whenever there is bright
sunshine, the image formed is intense enough to burn a spot on the card strip. Through the
day as the sun moves across the sky, the image moves along the card strip. Thus, a burnt trace
whose length is proportional to the duration of the sunshine is obtained on the strip.
Air Mass (AM): -
AM is used as a measure of the distance traveled by beam radiation through the
atmosphere before it reaches a location on the earth‟s surface.
It is defined as the ratio of the mass of the atmosphere through which the beam
radiation passes to the mass it would pass through if the sun is directly overhead (i.e. at its
zenith). The zenith angle
horizontal surface.
z is the angle made by the sun‟s rays with the normal to a
Since AM = sec z , AM 0 Extraterrestrial radiation, AM 1 the sun at its zenith &
17
AM 2 zenith angle of 60˚.
18
g
d
The intensity of solar radiation directly outside the earth‟s atmosphere on a horizontal surface
is almost constant and is equal to 1367 W/m2 and this is called solar constant. This entry
point into the atmosphere is called Air Mass -0 or AM-0, where 0 points out that there is no
air mass.
Azimuth: - An azimuth is an angular measurement in a spherical coordinate system. The
vector from an observer (origin) to a point of interest is projected perpendicularly onto a
reference plane; the angle between the projected vector and a reference vector on the
reference plane is called the azimuth. Azimuth is usually measured in degrees.
An example of an azimuth is the measurement of the position of a star in the sky. The
star is the point of interest, the reference plane is the horizon or the surface of the sea, and the
reference vector points to the north. The azimuth is the angle between the north point and the
perpendicular projection of the star down onto the horizon.
Measuring Instruments
Solar Radiation Data:-
1 Wh = 3600 J
I Hourly global radiation in kJ/m2-h.
I Hourly diffuse radiation in kJ/m2-h.
19
d H Daily diffuse radiation in kJ/m2-day.
Solar Radiation Geometry:-
Aim: - To find the beam energy falling on a surface having any orientation (horizontal
/ inclined). For this, convert the value of beam flux coming from the sun ( I bn ) to an
equivalent value corresponding to the normal direction to the surface (
Relationships for making this conversion is presented hereunder.
I bn cos ).
If is the angle between an incident beam of flux I bn and the normal to a plane
surface, then the equivalent flux falling normal to the surface is given by I bn cos .
The angle can be related by a general equation to
surface azimuth angle, declination and hour angle).
, , , , (latitude, slope,
1. δ ( in degrees) = 23.45 sin360
(284 n)Eqn.1
365
where - n is the day of the year.
It can be shown that
2. cos θ = sin φ (sin δ cos β + cos δ cos cos ω sin β) + cos φ (cos δ cos ω
cos β - sin δ cos sin β) + cos δ sin sin ω sin β ----------------- Eqn.2
Special cases of Eqn.2 are normally required. Some of these are:-
Case 1:- For a vertical surface, slope = 90˚
cos θ = sin φ cos δ cos cos ω - cos φ sin δ cos + cos δ sin sin ω ---------- Eqn.3
Case 2:- For a horizontal surface, slope = 0˚
cos θ = sin φ sin δ + cos φ cos δ cos ω ----------------- Eqn.4
The angle θ in this case is the zenith angle θz .
cos z = sin φ sin δ + cos φ cos δ cos ω
The compliment of the zenith angle is also used quite often in calculations. It is called solar
altitude angle (αa).
a 2
z
20
cos θ = sin φ (sin δ cos β + cos δ cos ω sin β) + cos φ (cos δ cos ω cos β - sin δ sin β)
= sin δ sin (φ – β) + cos δ cos ω cos (φ – β) ----------------- Eqn.5
Case 4:- For a vertical surface facing due south, slope = 90˚;
surface azimuth angle γ = 0˚
cos θ = sin φ cos δ cos ω - cos φ sin δ ----------------- Eqn.6
Case 5:- For an inclined surface facing due north, surface azimuth angle γ = 180˚
cos θ = sin δ sin (φ + β) + cos δ cos ω cos (φ + β) -----------------Eqn.7
The angle of incidence θ can also be expressed in terms of zenith angle θz , slope , surface
azimuth angle γ and solar azimuth angle γs. Braun and Mitchell have shown that
cos θ = cos θz cos β + sin θz sin β cos ( s – ) ----------------- Eqn.8
Solar azimuth angle γs:- It is the angle made in the horizontal plane between the horizontal
line due south and the projection of the line of sight of the sun on the horizontal plane. Thus it
gives the direction of the shadow cast in the horizontal plane by a vertical rod.
Solar azimuth angle γs = + ve if the projection of the line of sight is east of south
= - ve if the projection of the line of sight is west of south
In order to use Eqn. 8, it is necessary to first calculate θz and γs. θz is obtained from Eqn. 4,
while γs is obtained from the expression 8.
cos z = (cos θz sin φ - sin δ) / sin θz cos φ
Also, sin αa = sin sin + cos cos cos ω
Incident angle =
- αa 2
where, δ – declination, φ – latitude, θ – angle of incidence,
– surface azimuth angle, β – slope, ω – hour angle, θz – zenith angle
z – solar azimuth angle, αa – solar altitude angle.
Sunrise, Sunset and Day length:
cos ωs = -tan φ tan δ
ωs = hour angle corresponding to sunrise or sunset (in degrees)
21
For inclined surface facing due south, = 0º
ωst = cos-1 [-tan (φ – β) tan δ]
|ωst| = min [|cos-1 (-tan φ tan δ)|, | cos-1 { - tan (φ – β) tan δ} | ]
For inclined surface facing due north,
|ωst| = min [ |cos-1 (-tan φ tan δ)|, | cos-1 { - tan (φ + β) tan δ} | ]
Sunrise, Sunset and Day Length
For Horizontal Surface: The hour angle corresponding to sunrise or sunset (ωs) on a
horizontal surface can be found from eqn. 4 if we substitute the value of 90˚ for the zenith
angle. Thus we obtain
cos ωs = -tan φ tan δ
ωs = hour angle corresponding to
sunrise or sunset (in degrees) = cos-1 (-tan φ tan δ) -------- Eqn. 10
The above equation yields a positive and negative value for ωs , the positive value
corresponding to sunrise and negative to sunset. Since 15˚ of the hour angle is equivalent to
1 hour, the corresponding day length (in hours)
Day length, Smax =
where, ωs is in degrees.
2 ωs =
15
2 cos-1 (-tan φ tan δ) -------- Eqn. 11
15
For inclined surface facing due South (γ = 0):
The above eqn.11 can be used if the day lies between September 22 and March
21 and the location is in the northern hemisphere.
Between March 21 and September 22, the hour angle at sunrise or sunset would be
smaller in magnitude than the value given by eqn. 10 and is given as
ωst = cos-1 [-tan (φ – β) tan δ] ---------- Eqn. 12
|ωst| = min [|cos-1 (-tan φ tan δ)|, | cos-1 {- tan (φ – β) tan δ} |] ---- Eqn. 13
For inclined surface facing due North
|ωst| = min [|cos-1 (-tan φ tan δ)|, | cos-1 {- tan (φ + β) tan δ} |] ---- Eqn. 14
22
Empirical Equations for Predicting the Availability of Solar Radiation:
The best approach for estimating average solar radiation for a place: - Measure
solar radiation over a period of time at that place.
If this is not possible, data from nearby locations having a similar geography and
climate can be used.
In case, if both these approaches are not possible, one can use empirical relationships
linking the values of radiation, global or diffuse, with meteorological parameters like
sunshine hours, cloud cover and precipitation.
Sometimes, even if measurements of radiation are available, the data may not be in
the desired form. For e.g., the daily global radiation may be measured whereas hourly data
may be needed for some specific purposes. Again we may require the beam and diffuse
components explicitly out of the daily global radiation.
Attempts have been made by many researchers to develop empirical relationships for
such situations and these are
1. Monthly average daily global radiation
2. Monthly average daily diffuse radiation
3. Monthly average hourly global radiation
4. Monthly average hourly diffuse radiation
Monthly average daily global radiation:
Angstrom suggested that
Hg a b
S
………….. Eqn. A
Hc Smsx
Hg = monthly average of the daily global radiation on a horizontal surface at a
location ( kJ / m2 – day )
Hc = monthly average of the daily global radiation on a horizontal surface at the
same location on a clear day ( kJ / m2 – day )
23
Smsx = monthly average of the maximum possible sunshine hours per day at the
location, i.e., the day length on a horizontal surface (h)
a,b = constants
Because of difficulties in deciding what constitutes a clear day, Page suggested that
Hc in
eqn. A be replaced by Ho , the monthly average of the daily extraterrestrial radiation which
would fall on a horizontal surface at the location under consideration.
Hg a b
S
Eqn. B
Ho Smsx
In the above computation, the quantity
Ho is the mean value (H0) for each day of the month.
H0 is obtained by integrating over the day length as follows:
Ho = Isc [1 + 0.033 cos 360n
] sin sin cos cos cos dt ……Eqn. C 365
Isc = 1367 W / m2
Where, t 180
15
Hence, dt 180
d15
t is in hours and is in radians
12 360n s
Ho
Isc1 0.033cos 365
sin sin cos cos cos d
Ho 24
0.033 cos 360 n
sin sin cos cos sin ……Eqn. D Isc1 365
s s
The dates on which the value of
Ho Ho are as follows:
January 17 February 16 March 16
April 15 May 15 June 11
July 17 August 16 September 15
s
24
1
Correlation: For predicting the daily global radiation at locations all over the world
including locations in India.
Hg
a1
b S
Ho Smsx
where
a1 -0.309 + 0.539 cos - 0.0693 EL
S + 0.290 S
max
b1 1.527 – 1.027 cos + 0.0926 EL
S - 0.359 S
max
EL = Elevation of location above MSL (in kilometers).
Monthly Average Daily Diffuse Radiation:
The equation shown below shows that the daily diffuse-to-global radiation ratio can
be correlated against the daily global-to-extraterrestrial radiation ratio.
Either of the two equations or both can be used for India to calculate the Monthly
Average Daily Diffuse Radiation.
Hd 1.411 1.696 H g
H g Ho
by Modi and Sukhatme
Hd 0.8677 H
S 0.7365
S
by Garg and Garg
g max
Hg K
Ho
Monthly Average Clearness Index
Monthly Average Hourly Global Radiation:
I g
Hg
o a b cos/ f c .................................... by Gueymard
Ho
Where: a = 0.409 + 0.5016 sin ( s - 60˚)
b = 0.6609 – 0.4767 sin ( s - 60˚)
T
I
25
o
H
H
c
s
g
Normalizing factor,
s
f a 0.5b 180
sin s
cos
sin
s s cos 180
s
I Monthly Average of the hourly global radiation on a horizontal surface (kJ / m2-h)
I Monthly Average of the ET radiation on a horizontal surface (kJ / m2-h)
Note: Wherever needed, an hourly value (kJ / m2-h) can be calculated from an instantaneous
value by taking the instantaneous value (kW / m2) at the mid-point of the hour and
multiplying by 3600.
Monthly Average Hourly Diffuse Radiation:
I d Io
Hd Ho
………. by Liu and Jordan
Id (a bcos) I0
Hd H 0
……….by Satyamurthy and Lahiri
H
Where: a 0.4922 0.27 /(H / H ) for 0.1 d 0.7
d g g
H or a 0.76 0.113/(H / H )for 0.7 d 0.9
d g g
b 2(1 a)(sin s s coss ) /(s 0.5sin 2s )
Also,
I I 1 0.033 cos
360 n sin sin cos cos cos Hourly ET radiation.
O SC
365
Solar Radiation on Tilted Surfaces:
Most solar equipment like flat-plate collector (which is used for absorbing solar
radiation) is tilted at an angle to the horizontal. It therefore becomes necessary to calculate
the flux which falls on a tilted surface. This flux is the sum of the beam and diffuse radiation
falling directly on the surface and the radiation reflected onto the surface from the
surroundings.
26
T
I
I I
I
I I
Beam Radiation
Beam radiation flux falling on a tilted surface (cos θ)
cos θ = sin δ sin (φ – β) + cos δ cos ω cos (φ – β)
Beam radiation flux falling on a horizontal surface (cos θz)
cos θz = sin φ sin δ + cos φ cos δ cos ω
Hence tilt factor for beam radiation, rb is given as
rb = cos
cos z
sin sin( ) cos cos cos( )
sin sin cos cos cos
Valid only for a tilted
surface with 0 º
Diffuse Radiation
rd (1 cos ) / 2 valid for any tilted surface with a slope and
(1 cos ) / 2 is the radiation shape factor for a tilted surface w.r.to the sky.
Reflected Radiation
rr (1 cos ) / 2 valid for any tilted surface with a slope and
(1 cos ) / 2 is the radiation shape factor for a tilted surface w.r.to the surrounding ground
and (is the diffuse reflectivity) = 0.2, for concrete or grass surface.
Flux on Tilted Surface:
The flux IT falling on a tilted surface at any instant is given by
IT Ib rb Id rd (Ib Id )rr
To calculate hourly radiation falling on a tilted surface for the value of taken at the
mid-point of the hour:
T 1
rb
rd rr
g g g
To calculate monthly average hourly value I if the calculations are done for the
representative day of the month:
T d d
1 r r r b d r
Id I Id
I
I
I
27
H
H H
s
H
H H
Where rb rb on the representative day
rd rd and rr rr
To calculate the daily radiation falling on a tilted surface:
T 1
Rb
Rd Rr
g g g
For a south facing surface ( = 0º ),
R st sin sin( ) cos sin st cos( )
b sin sin cos cos sin
Rd rd and Rr rr
st and s are the sunrise or sunset hour angles (in radians) for the tilted
surface and a horizontal surface respectively.
To calculate monthly average daily radiation falling on a tilted surface if the values are
calculated for the representative day of the month:
T d d 1 R R R
b d r
g g g
where
Rb Rb on the representative day;
Rd Rd and
Rr Rr
Hd H Hd
H
s
H
H
28
SOLAR COLLECTORS
Introduction
A solar collector is a device for collecting solar radiation and transfers the energy to a
fluid passing in contact with it.
Utilization of solar energy requires solar collectors. They are broadly classified into:
1. Non concentrating or flat plate type solar collector
Collector area is the same as the absorber area.
Simple in design.
Has no moving part.
Requires less maintenance.
Used for both beam and diffuse solar radiation.
Temperature range 40˚ C - 100˚ C.
2. Concentrating or focusing type solar collector
Collector area is greater than the absorber area.
Here higher temperature can be obtained.
For generation of medium pressure steam.
Better efficiency than the flat plate type.
Principle of operation of a collector
Expose a dark surface to solar radiation so that the radiation is absorbed. The part of
the absorbed radiation is then transferred to a fluid like air or water.
Flat plate collector
It consists of an absorber plate on which the solar radiation falls after coming through
a transparent cover, made of glass. The absorbed radiation is partly transferred to a liquid
flowing through tubes which are fixed to the absorber plate. This energy transfer is the useful
heat gain. The remaining part of the radiation absorbed in the absorbed plate is lost by
convection and re-radiation to the surroundings from the top surface, and by conduction
through the back and the edges. The transparent cover helps in reducing the losses by
convection and re-radiation, while thermal insulation on the back and the edges helps in
29
reducing the conduction heat loss. A liquid flat-plate collector is usually held tilted in a fixed
position on a supporting structure, facing south if located in the northern hemisphere.
In order to reduce the heat lost by re-radiation from the top of the absorber plate of a
flat-plate collector, it is usual to put a selective coating on the plate. The selective coating
exhibits the characteristic of a high value of absorptivity for incoming solar radiation and a
low value of emissivity for out-going re-radiation. As a result, the collection efficiency of the
flat-plate collector is improved.
Based on the type of heat transfer fluid used, FPC may be classified as Liquid Heating
Collector and Air Heating Collector(solar air heater).
Applications of solar air heaters
For heating buildings.
For drying agricultural produce.
Heating green houses.
Using air heaters as the heat source for a heat engine such as a Brayton cycle.
Flat plate collector
The basis parts of a liquid flat plate collector are
(a) the absorber plate (made of thin metal(Cu) sheet of thickness from 0.2 to 0.7 mm).
(b) the tubes fixed to the absorber plate through which the liquid to be heated flows (made of
metal(Cu) with = 1 to 1.5 cm / liquid used – water. Sometimes mixtures of water and
ethylene glycol are used if ambient temperatures below 0˚ C are likely to be encountered /
pitch of the tubes = 5 to 12 cm).
(c) the transparent cover (Property of the cover – highly transparent to incoming solar
radiation and at the same time, opaque to the long wavelength re-radiation emitted by the
absorber plate / made of toughened glass with low ferric oxide / 4 or 5 mm thickness).
(d) the collector box (made of Al with an epoxy coating on the outside for protection / the
bottom and sides are usually insulated by mineral wool, rock wool or glass wool with a
covering of Al foil and has a thickness ranging from 2.5 to 8 cm).
Advantages:- Utilizes both beam and diffuse components of solar radiation, simple stationary
design, less maintenance.
Disadvantages:- Because of the absence of optical concentration, the area from which heat is
30
lost is large. As a result, the collection efficiency is low.
Principle of operation:- It consists of an absorber plate on which the solar radiation falls after
coming through a transparent cover, made of glass. The absorbed radiation is partly
transferred to a liquid flowing through tubes which are fixed to the absorber plate. This
energy transfer is the useful heat gain. The remaining part of the radiation absorbed in the
absorbed plate is lost by convection and re-radiation to the surroundings from the top surface,
and by conduction through the back and the edges. The transparent cover helps in reducing
the losses by convection and re-radiation, while thermal insulation on the back and the edges
helps in reducing the conduction heat loss. A liquid flat-plate collector is usually held tilted in
a fixed position on a supporting structure, facing south if located in the northern hemisphere.
In order to reduce the heat lost by re-radiation from the top of the absorber plate of a flat-
plate collector, it is usual to put a selective coating on the plate. The selective coating exhibits
the characteristic of a high value of absorptivity for incoming solar radiation and a low value
of emissivity for out-going re-radiation. As a result, the collection efficiency of the flat-plate
collector is improved. Based on the type of heat transfer fluid used, FPC may be classified as
Liquid Heating Collector and Air Heating Collector (solar air heater).
Applications of solar air heaters
For heating buildings.
For drying agricultural produce.
Heating green houses.
Using air heaters as the heat source for a heat engine such as a Brayton cycle.
Performance Analysis of Flat Plate Collector
The analysis is done for steady state condition in which the liquid is flowing through tubes
bonded on the under-side of the absorber plate.
qu Ap S ql , where qu useful heat gain (i.e., rate of heat transfer to the
working fluid)
S = incident solar flux absorbed in the absorber plate
S = Ib rb ( )b I d rd (Ib Id )rr ( )d
= transmissivity; = absorptivity; Ap = area of the absorber plate
31
b Transmissivity-absorptivity product for beam radiation falling on the collector. The
transmissivity-absorptivity product is defined as the ratio of the flux absorbed in the absorber
plate to the flux incident on the cover system.
ql = rate at which heat is lost by convection and re-radiation from the top and by
conduction and convection from the bottom and sides.
Instantaneous Collection Efficiency, i qu
Ac IT
; where Ac Collector Gross Area.
Stagnation efficiency:- If the liquid flow rate through the collector is stopped, then there is
no useful heat gain and the efficiency is zero. In this case, the absorber plate attains a
temperature such that Ap S ql . This temperature is the highest that the absorber that the plate
can attain. Knowledge of the stagnation temperature is useful as an indicator for comparing
different collector designs.
Effective transmittance absorptance product ( ( )
1 (1 )d
d = diffuser reflectivity of the cover system = 0.16 for one glass cover system.
= 0.24 for two glass cover system.
= 0.29 for three glass cover system.
Overall loss coefficient and heat transfer correlations
Heat lost from the collector, ql Ul Ap (Tpm Ta )
Ul overall loss coefficient =Ut Ub Us ; (= top loss coefficient + bottom loss coefficient
+ side loss coefficient)
Ap Area of the absorber plate
Tpm Average temp. of the absorber plate; Ta Temp. of the surrounding air
ql qt qb qs
qt rate at which heat is lost from the top = Ut Ap (Tpm Ta )
qb rate at which heat is lost from the bottom = Ub Ap (Tpm Ta )
qs rate at which heat is lost from the sides = Us Ap (Tpm Ta )
U l is an important parameter since it is a measure of all the losses and typical values range
32
Top loss coefficient (U t ):
The top loss coefficient is evaluated by considering convection and re-radiation
losses from the absorber plate in the upward direction. Assumption: one-dimensional, steady,
temp. drop across the thickness of the covers is negligible.
In a steady state, the heat transferred by convection and radiation between (i) the absorber
plate and the first cover (ii) the first cover and the second cover (iii) the second cover and the
surrounding must be equal. Hence,
q (T 4 T 4 ) (T 4 T 4 ) t h (T T ) pm c1
h
(T T ) c1 c2 h (T T ) (T 4 T 4 )
A pc1 pm c1
1 1
c1c2 c1
c2 1 1
w c 2 a c c2 sky
p p c
1
c c
1
hp c1 convective heat transfer coefficient between the absorber plate & the first cover
hc1c 2 convective heat transfer coefficient between the first and second covers.
hw convective heat transfer coefficient between the top cover and surrounding air
Tc1 ,Tc 2 temperatures attained by two covers
Tsky Ta 6
p emissivity of the absorber plate for long wavelength radiation
c emissivity of the covers for long wavelength radiation.
The above equations constitute a set of three non-linear equations which have to be
solved for the unknowns ql ,Tc1 and Tc 2 . However, before this can be done it will be
necessary to have some correlations for calculating the convective heat transfer coefficients
hpc1 , hc1c 2 and hw , and the sky temperature Tsky .
Heat Transfer Coefficient between Inclined Parallel Surfaces:
The natural convection heat transfer coefficient for the enclosed space between the
absorber plate and the first cover or between two covers is calculated by using one of the
following correlations:
NuL 1 ; RaL cos < 1708
1708
33
pm a
pm a
w
NuL 0.229 ( RaL cos )0.252 ; 5900 < Ra L cos < 9.23 x 104
NuL 0.157 ( RaL cos )0.285 ; 9.23 x 104 < Ra L cos < 106
The characteristic dimension L is the spacing between the surfaces, while properties
are evaluated at the arithmetic mean of the surface temperatures.
Heat Transfer Coefficient at the top cover:
The convective heat transfer coefficient ( hw ) at the top cover is often referred to as
the wind heat transfer coefficient. It is calculated using the relation,
2
hw 8.55 2.56 V∞ ; h is in W/m – K and V∞ is in m/s.
Bottom loss coefficient (Ub ):
The bottom loss coefficient is evaluated by considering conduction and convection
losses from the absorber plate in the downward direction through the bottom of the collector.
Assumption: one-dimensional, steady. In most cases, the thickness of insulation provided is
such that the thermal resistance associated with conduction dominates. Thus neglecting
convective resistances, we have
Ub b
where ki thermal conductivity of the insulation
b thickness of insulation
Side loss coefficient (U s ):
Side loss coefficient is always much smaller than the top loss coefficient.
Assumption: one-dimensional, steady, conduction resistance dominates.
If the dimensions of the absorber plate is L1 xL2 and the height of the collector casing is L3 ,
then the area across which heat flows sideways is 2L1 L2 L3 . The temperature drop across
which the heat flow occurs varies from T T at the absorber plate level to zero both at
the top and bottom. Assuming, therefore, that the average temperature drop across the side
insulation is T T / 2 and that the thickness of the side insulation is s , we have,
q 2L (L
L )k (Tpm Ta )
s 3 1 2 i 2
s
ki
34
i
Useful heat gain for the flat plate collector (qu):
qu FR Ap [ S – UL ( Tfi – Ta )]
FR = Collector heat removal factor ; Ap = Area of the collector plate
S = Flux absorbed in the absorber plate = Ib rb b ; UL = Top loss coefficient
Tfi = Collector fluid temperature ; Ta = Ambient temperature
Collector efficiency (ηi):
η = qu
Ib rb
Focusing or Concentrating Collectors
Used for higher temperatures, from 100 - 400˚ C or above 400˚ C.
It consists of a concentrator and receiver. The concentrator is a mirror reflector
(optical system) having the shape of a cylindrical parabola. It focuses the sunlight on
to its axis, where it is absorbed on the surface of the absorber tube and transferred to
the fluid flowing through it.
A concentric glass cover around the absorber tube helps in reducing the convective
and radiative losses to the surroundings.
In order that the sun‟s rays should always be focused on to the absorber tube, the
concentrator has to be rotated. This movement is called tracking.
One axis tracking: In the case of cylindrical parabolic concentrators (CPC), rotation
about a single axis is generally required. In CPC, fluid temperatures up to 400˚ C can
be achieved.
Two axis tracking: Temperatures more than 400˚ C is obtained using Paraboloid
35
Concentrating Collectors (PCC) which has a point focus. These PCC require 2-
axis tracking so that the sun is in line with the focus and the vertex of the paraboloid.
36
Disadvantages:
Because of the presence of an optical system, a concentrating collector has to track
the sun so that the beam radiation is directed on to the absorber surface. The need for
tracking introduces a certain amount of complexity in the design.
Maintenance requirements are also increased. All these factors add to the cost.
Much of the diffuse radiation is lost because it does not get focused.
Definitions:
Concentrator: Optical system which directs the solar radiation on to the absorber
Receiver: Consists of the absorber, its cover and the accessories.
Aperture (W): It is the plane opening of the concentrator through which the solar radiation
passes.
Area concentration ratio(C) / Geometric concentration ratio / Concentration ratio: It is
the ratio of the effective area of the aperture to the surface area of the absorber. C = 1
(is the limiting case for a flat-plate collector) to a few thousand for a paraboloid dish.
Intercept factor (γ): It is the fraction of radiation which is reflected or refracted from the
concentrator and is incident on the absorber. γ is generally close to unity.
Acceptance angle (2 a ): It is the angle which beam radiation may deviate from the
normal to the aperture plane and yet reach the absorber. Collectors with large acceptance
angles require only occasional adjustments, while collectors with small acceptance angles
have to be adjusted continuously.
Absorber area Aabs : It is the total area that receives the concentrated solar radiation. It is
the area from which the useful energy can be removed.
37
l l p pm a
Optical efficiency o : It is defined as the ratio of energy absorbed by the absorber to the
energy incident on the concentrator‟s aperture.
Thermal efficiency t : It is defined as the ratio of useful energy delivered to the energy
incident on the aperture.
Types of concentrating collectors:
1. Flat-plate collector with plane reflectors
2. Compound parabolic collector
3. Cylindrical parabolic collector
4. Collector with fixed circular concentrator and moving receiver
5. Fresnel lens concentrating collector 6. Paraboloid dish collector.
Thermal and Performance Analysis of Concentrating Collectors: Under steady-state
condition,
qu = Aa S ql (assumption: diffuse radiation is negligible) …..Eqn. 1
where q = U A T T ql Ul Do L(Tpm Ta )
…..Eqn. 2
qu
Aa S
Ul (TC
pm Ta )
…..Eqn. 3
qu rate of useful heat gain ; ql = rate of heat loss from the absorber.
Aa effective aperture area of the concentrator = (W- Do )L
(Also:- Aa aperture area of the concentrator = (W- Dco )L)
Dc0 outer diameter of the transparent cover
Dci inner diameter of the transparent cover
Ap area of the absorber surface or receiver = Do L
S = solar beam radiation per unit effective aperture area absorbed in the absorber
Ul overall loss coefficient
C = concentration ratio = Aa
Ap
= (W Do )
Do
38
Do outer diameter of absorber tube ; Di = inner diameter of absorber tube
Tpm average temperature of the absorber tube
Ta temperature of the surrounding air ;
Tc = temperature attained by the cover
Ib instantaneous beam radiation on a horizontal surface
rb tilt factor for instantaneous beam radiation
I d
rd
instantaneous diffuse radiation on a horizontal surface
tilt factor for instantaneous diffuse radiation
.
r = rim angle ; m = fluid mass flow rate in kg/hr ; C p sp. heat at constant pressure ;
T fi = inlet fluid temperature ; T fo = outlet fluid temperature
hp c = convective ht. tr. coeff. betn. the absorber tube and the glass cover
Collector efficiency factor:
F 1
…..Eqn. 4
1 U l U
Do
D h l i f
h f = ht. tr. coeff. on the inside surface of the tube
Useful heat gain rate:
q F W Ul T
T …..Eqn. 5
u R Do LS
C fi
a
Do
S = I brb ( . )b Ibrb b W D …..Eqn. 6
o
Ib rb beam radiation on the plane of the aperture per unit time per unit area
specular reflectivity of the concentrator surface ; intercept factor
39
3 4
Instantaneous collection efficiency, i (Ib rb
qu
I d r d
)WL
…..Eqn. 8
The instantaneous collection efficiency can also be calculated on the basis of beam radiation
alone, in which case
ib
qu
Ib rbWL …..Eqn. 9
Overall Loss Coefficient (U l ) and Heat Transfer Correlations:
The calculation of U l is based on convection and reradiation losses. The absorber tube and
the glass cover around it constitute a system and hence we have
q D
T 4 T 4
Heat loss rate per unit length, l h
L
pc Tpm Tc Do 1 0 pm
D 1
c
…..Eqn. 10
0
p Dci c 1
= h T T D D T 4 T 4 …..Eqn. 11 w c a co co c c sky
Eqns. 10 and 11 are a set of two non-linear equations which have to be solved for the
unknowns ql L and Tc after substituting the values of hp c and hw .
= Stefan Boltzmann Constant = 5.67 x 10-8 W/m2-K4.
Heat Transfer Coefficient between the absorber tube and the cover:
The natural convective heat transfer coefficient hp c for the enclosed annular space
between a horizontal absorber tube and a concentric cover is calculated using
k eff = 0.317 Ra* 1 4
k
…..Eqn. 12
where keff = Effective thermal conductivity – It is defined as the thermal conductivity that the
motionless air in the gap must have to transmit the same amount of heat as the moving air.
Ra* = modified Rayleigh number related to the usual Rayleigh number by
Ra * 1 4
lnDci
b 1
Do
1
5 4
Ra1 4
…..Eqn. 13
40
D3 5
ci
eff eff
o
D3 5 o
The characteristic dimension used for the calculation of the Rayleigh number is the radial gap
b D D / 2. Properties are evaluated at the mean temperature T T / 2. ci o pm c
Note:- k cannot be less than k. Hence k
yields a value less than unity.
k is put equal to unity if the use of eqn. 13
hpc 2keff
…..Eqn. 14. The limitations on using eqn. 12 are that Ra*
should be less than 107 and b should be less than 0.3 D .
Heat Transfer Coefficient on the outside surface of the cover:
The convective heat transfer coefficient hw on the outside surface of the cover (wind
heat transfer coefficient) is calculated using the equation
Nu C1 Re n …..Eqn. 15 (Assumption: wind velocity is at angles to the axis of the
collector.
Where C1 and n are constants having the following values:
For 40 < Re < 4000, C1 =0.615, n =0.466
For 4000 < Re < 40000, C1 =0.174, n =0.618
For 40000 < Re < 400000, C1 =0.0239, n =0.805
Characteristic dimension used in eqn. 15 is Dco . Properties are to be evaluated at the mean
temperature Tc Ta / 2. Re 4Dco and Nu hw .L K .
Performance Analysis of Liquid Flat-Plate Collectors
The performance analysis is done for a steady state condition in which the liquid is flowing
through tubes bonded on the under-side of the absorber plate.
An energy balance on the absorber plate yields the following equation for a steady state
qu Ap S ql -------------- Eqn 1
Where qu useful heat gain (i.e., rate of heat transfer to the working fluid)
Do lnDci D0
41
2 2
= absorptivity of the absorber plate
= transmissivity- absorptivity product
Ap = area of the absorber plate; b = beam radiation; d = diffuse radiation
ql = rate at which heat is lost by convection and re-radiation from the
top, and by conduction and convection from the bottom and sides.
In order to find qu , it is necessary to derive expressions to calculate ( )b , ( )d
and ql .
Instantaneous Collection Efficiency:
i qu
Ac IT
= usefulheatgain
radiationincidentonthecollector
-------------- Eqn 3
Ac Collector Gross Area (the area of the topmost cover including the frame).
Stagnation Temperature: If the liquid flow rate through the collector is stopped, there is no
useful heat gain and the efficiency is zero. In this case, the absorber plate attains a
temperature such that Ap S ql . This temperature is the highest temperature that the absorber
plate can attain and is called as the stagnation temperature. Knowledge of the stagnation
temperature is useful as an indicator for comparing different collector designs. It also helps in
choosing proper materials for construction of the collector.
Transmissivity of the cover system:
r a
Where r transmissivity obtained by considering only reflection and refraction
= 1
( )
2 rI rII
rI
1 I
1 I and
rII
1 II
1 II
sin 2 ( ) tan2 ( )
2 1 and 2 1 I sin 2 ( )
1
II tan2 ( ) 1
42
1 angle of incidence; 2 angle of refraction
I and II are the reflectivities of the two components of polarization.
If there are M covers, the exponent is multiplied by M; c thickness of the transparent
cover; K = extinction coefficient = 4 to 25
desirable.
m 1 for different quality of glass. A low value is
Effective transmittance absorptance product ( ( )
1 (1 )d
Diffuse reflectivity of the cover system = d = 0.16 for one glass cover system
= 0.24 for two glass cover system
= 0.29 for three glass cover system
Overall loss coefficient and heat transfer correlations: Overall loss coefficient is the sum of
top loss coefficientU t , bottom loss coefficient Ub and side loss coefficientU s .
Heat lost from the collector, ql
U l
Ul Ap (Tpm Ta )
overall loss coefficient = Ut Ub Us
Ap Area of the absorber plate
Tpm Average temperature of the absorber plate
Ta Temperature of the surrounding air
ql qt qb qs
qt Ut Ap (Tpm Ta ); qb Ub Ap (Tpm Ta) ; qs Us Ap (Tpm Ta )
U l U t Ub U s
The overall loss coefficient is an important parameter since it is a measure of all the losses.
Typical values range from 2 to 10 W/m2-K.
Top loss coefficient:
The top loss coefficient Ut is evaluated by considering convection and re-
radiation losses from the absorber plate in the upward direction. A schematic diagram for a
two cover system is shown.
In a steady state, the heat transferred by convection and radiation between (i) the absorber
plate and the first cover (ii) the first cover and the second cover (iii) the second cover and the
43
surroundings must be equal.
44
Hence,
q
(T 4 T 4 )
(T 4 T 4 ) t h (T T ) pm c1
h
(T T ) c1 c2 h (T T ) (T 4 T 4 )
A pc1 pm c1
1 1
c1c2 c1
c2 1 1
w c 2 a c c2 sky
p p c
1
c c
1
hp c1 convective heat transfer coefficient between the absorber plate and the I cover
hc1c 2 convective heat transfer coefficient between the I and II covers.
hw convective heat transfer coefficient between the top cover and surrounding air
Tc1 ,Tc 2 temperatures attained by two covers
Tsky Ta 6 in Kelvin.
p emissivity of the absorber plate for long wavelength radiation
c emissivity of the covers for long wavelength radiation.
The above equation constitute a set of three non-linear equations (A nonlinear
equation does not produce a straight line and the exponent is to the second power or more),
which have to be solved for the unknowns ql ,Tc1 & Tc 2. However, before this can be done it
will be necessary to have some correlations for calculating the convective heat transfer
coefficients hpc1 , hpc 2 , hw & Tsky.
Heat Transfer Coefficient between Inclined Parallel Surfaces:
The natural convective heat transfer coefficient for the enclosed space between the
absorber plate and the first cover or between two covers is calculated by using one of the
following correlations:-
NuL 1 ; RaL cos < 1708
1708
NuL 1 + 1.446 1 Ra
cos ; 1708 < Ra L cos < 5900
L
NuL 0.229 ( RaL cos )0.252 ; 5900 < Ra L cos < 9.23 x 104
NuL 0.157 ( RaL cos )0.285 ; 9.23 x 104 < Ra L cos < 106
Nu and Ra are the Nusselt & Rayleigh Nos. respectively. The characteristic dimension L is
the spacing between the surfaces, while properties are evaluated at the arithmetic mean of the
surface temperatures.
45
w
Heat Transfer Coefficient at the top cover:
The convective heat transfer coefficient ( hw ) at the top cover is also known as the
wind heat transfer coefficient. It is calculated using the following correlation:
2
hw 8.55 2.56 V∞ ; h is in W/m – K and V∞ is in m/s.
Bottom loss coefficient:
The bottom loss coefficient Ub is calculated by considering conduction and
convection losses from the absorber plate in the downstream direction through the bottom of
the collector.
In most cases, the thickness of the insulation provided is such that the thermal resistance
associated with conduction dominates. Thus neglecting the convective resistances, we have
Ub b
Where ki thermal conductivity of the insulation; b thickness of the
insulation.
Side loss coefficient:
Here also, it is assumed that the conduction resistance dominates and the flow of heat
is 1-Dimensional and steady. The side loss coefficient is always much smaller than the top
loss coefficient.
If the dimensions of the absorber plate are L1 x L2 and the height of the collector casing is
L3, then the area across which the heat flows sideways is 2(L1 x L2)L3. The temperature drop
across which the heat flow occurs varies from ( Tpm Ta ) at the absorber plate level to zero
both at the top and bottom. Assuming, therefore, that the average temperature drop across the
side insulation is ( Tpm Ta ) / 2 and that the thickness of the side insulation is s , we have
q 2L (L
L )k (Tpm Ta )
s 3 1 2 i 2
Thus, from eqn., qs Us Ap (Tpm Ta )
U L1 L2 L3 k i
s L L 1 2 s
Useful heat gain for the flat plate collector (qu):
qu FR Ap [ S – UL ( Tfi – Ta )]
FR = Collector heat removal factor
Ap = Area of the collector plate
S = Flux absorbed in the absorber plate = Ib rb b
UL = Top loss coefficient
s
ki
46
pm a
T
i
i
Ta = Ambient temperature
Collector efficiency (ηi):
η = qu
Ib rb
Collector Heat Removal Factor and Concentrating Collector
Collector heat-removal factor (FR): FR is an important design parameter since it is a
measure of the thermal resistance encountered by the absorbed solar radiation in reaching the
collector fluid.
FR represents the ratio of the actual heat gain rate to the gain which would occur if the
collector absorber plate was at the temperature of collector fluid temperature (Tfi)
everywhere. FR value ranges between 0 and 1.
Useful heat gain for the flat plate collector (qu):
qu FR Ap [S – Ul (Tfi – Ta)] …. Hottel-Whiller-Bliss equation
FR = Collector heat removal factor
Ap = Area of the collector plate
Ul = Top loss coefficient
Tfi = Inlet fluid temperature
Ta = Ambient temperature
S = Flux absorbed in the absorber plate =
Ib rb ( )b
Collector efficiency (ηi):
η = qu
Ib rb
Empirical Equation for Top Loss Coefficient:
1
M 1
T 2
T 2 T
Ta t T
T 0.252 h 1
2M f 1
C pm a
M
pm M f
p 0.0425M 1 p c
w
U pm
47
w
M = Number of glass covers
C = 204.429 cos 0.252 / L0.24 and L = spacing in metre
f = 30 T a
1 0.091M and h 5.7 3.8V h h2 316.9 w w
Concentrating Collector: - for temperatures up to 400˚C.
1. Concentration of solar radiation is achieved using a reflecting arrangement of
mirrors or a refracting arrangement of lenses.
2. The optical system directs the solar radiation on to an absorber of smaller area
which is usually surrounded by a transparent cover.
3. Because of the presence of an optical system, a concentrating collector has to track
the sun so that the beam radiation is directed on to the absorber surface. The need for some
form of tracking introduces a certain amount of complexity in the design. Also the
maintenance requirements are increased, which adds to the cost. An added disadvantage is
the fact that much of the diffuse radiation is lost because it does not get focused.
Definitions:
Concentrator: optical subsystem which directs the solar radiation on to the absorber
Receiver: subsystem consisting of the absorber, its cover and other accessories.
Overall Loss Coefficient (U l ) & Heat Tr. Correlations for Concentrating Collectors:
Assumption: Absorber tube & the glass cover around it constitute a system of long,
concentric tubes.
q D
T 4 T 4 l h
L
pc Tpm Tc Do 1 o pm
D 1 c
----------C.1
o
p Dci c 1
h T T D D T 4 T 4 -------------C.2 w c a o co c c sky
ql heat loss rate per unit length; L
p
emissivity of the absorber tube surface
hpc convective heat transfer coefficient between the absorber tube and the glass cover
Tpm average temperature of the absorber tube; Tc temperature attained by the cover
Do outer φ of the absorber tube; Dci inner φ of the glass cover; Ta ambient temp.
c emissivity of the glass cover; hw wind heat transfer coefficient in W/m2-K.
9
48
SOLAR THERMAL TECHNOLOGIES
UNIT 4
SOLAR THERMAL TECHNOLOGIES
SUBJECT CODE: SME1602
SUBJECT NAME: WIND AND SOLAR ENERGY
Energy can be stored as potential, kinetic, chemical, electromagnetic, thermal, etc. ... Examples of
chemical energy storage systems include batteries, flow batteries, and fuel cells. Mechanical (kinetic
and potential) energy storage systems include pumped storage hydropower, flywheels, and
pressurized gas storage systems.
Thermal energy storage (TES) is a technology that stocks thermal energy by heating or cooling
a storage medium so that the stored energy can be used at a later time for heating and cooling
applications for power generation. TES systems are used particularly in buildings and in industrial
processes.
Major problem associated with the utilization of solar energy is its availability.
Most applications require ‘energy storage’ system.
The purpose of ‘energy storage’ system is to store energy when it is in excess of the requirement of an
application and to make it available for extraction when the supply of solar energy is absent or
inadequate.
Energy storage can be in the following forms
Thermal energy – can be stored as sensible heat or as latent heat.
Electrical energy
Mechanical energy
Chemical energy
SENSIBLE HEAT STORAGE
It is usually done in an insulated container containing a liquid like water or a porous solid in the form of
pebbles or rocks.
The first type is used for liquid collectors while the second type is compatible with air heaters.
Sensible heat storage systems operate over a range of temperatures.
Classification of Thermal energy storage systems (TES)
Sensible heat storage: Heating a liquid or solid which does not change phase. The quantity of heat
stored is proportional to the temperature rise of the material. If T1 and T2 represent the lower and higher
temperature, V the volume and ρ the density of the storage material, and Cp the specific heat, then the
energy stored Q is given by:
Latent heat storage (Phase change heat storage): In this system, heat is stored in a material when it
melts, and heat is extracted from the material when it freezes. Heat can also be stored when a liquid
changes to gaseous state, but as the volume change is large, such a system is not economic.
The amount of energy stored in this case depends upon the mass and the latent heat of fusion of the
material. Thus, E = m.λ ; λ = latent heat of fusion.
Latent heat storage systems operate essentially at the temperature at which the phase change takes
place.
T2
T1Q= V Cp dT
Mechanical Energy Storage: Storage is done in large sized flywheels or in compressed air.
Compressed air is stored in large underground chambers.
Electrical Energy Storage: Storage is in the form of electric batteries (lead – acid battery storage).
Chemical Energy Storage: Using heat to induce a certain chemical reaction and then storing the
products. The heat is released when the reverse reaction is made to occur.
Solar pond: A novel device which combines the functions of both collection and storage is the solar
pond.
It consists of an span of water about a meter or two in depth, in which salts like sodium or
magnesium chloride are dissolved.
The concentration of the salt is more at the bottom and less at the top.
Because of this, the bottom layers of water are denser than the surface layers even if they are
hotter and natural convection does not occur.
Thus, the heat from the sun’s rays absorbed at the bottom of the pond is retained in the lower
depths, and the upper layers of water act like a thermal insulation.
SENSIBLE HEAT STORAGE
In sensible heat storage systems, energy is stored or extracted by heating or cooling a liquid or solid which
does not change its phase during the process.
Liquids used: water, heat transfer oils, inorganic molten salts
Solids used: rocks, pebbles, refractories – material is invariably in porous form. Heat is stored or extracted
by the flow of a gas or liquid through the pores or voids.
Choice of the substance depends on the temperature level of the application.
For temperatures below 100 ̊C – water is used.
For temperatures around1000 ̊C – refractory bricks are used.
Advantage of sensible heat storage: simpler in design than latent heat or thermo- chemical storage.
Disadvantage: 1. Bigger in size. 2. They cannot store or deliver energy at a constant temperature.
SENSIBLE HEAT STORAGE – LIQUIDS
Water is the most commonly used medium in a sensible heat storage systems.
Most solar water heating and space heating systems use hot water storage tanks
located either inside or outside the buildings or underground.
Size of the tanks - few 100 litres to a few 1000 cubic meters.
General thumb rule: 75 -100 litres of storage per square meter of collector area.
Storage tanks are made of steel, concrete and fibreglass.
Tanks should be suitably insulated with glass wool, mineral wool or polyurethane.
Thickness of insulation: 10 – 20 cm.
Because of the above, the cost of the insulation represents a significant part of the total cost of the sensible
heat storage.
It is possible to store water at temperatures a little above 100 ̊C by using pressurized tanks.
In order to reduce the cost of water storage systems, naturally occurring underground aquifers which
already contain water is used.
In such systems, the need for building a storage tank is eliminated.
For storing energy, hot water is pumped into the aquifer through an injection well.
At the same time, cold ground water is displaced through another well.
For withdrawing energy, the reverse procedure is followed.
Heat transfer oils: Used for intermediate temperatures ranging from 100 – 300 ̊C.
Eg: Servotherm is used in India.
Disadvantages: 1. The main problem associated with the use of heat transfer oils is that they tend to
degrade with time.The degradation is particularly serious if they are used above their recommended
temperature limit.
2. The use of oils also presents safety problems since there is a possibility of ignition above their flash
point. For this reason, it is recommended to use the systems with inert gas cover.
1. Cost of the heat transfer oil, which ranges from 60 – 120 per litre (of Indian brands). Hence these are
used in small storage systems
SOLAR COOKER
An important domestic thermal application is that of cooking.
SOLAR COOKER
Box type cooker Dish type cooker
(for domestic purpose) (for community purpose)
A slow cooking device suitable for domestic purposes.
It consists of a rectangular enclosure
Insulated at the bottom and sides with one or two glass covers on the top. Solar radiation enters through the
top and heats up the enclosure in which the food to be cooked is placed in shallow vessels.
Temperatures around 100 ˚C can be obtained in these cookers on sunny days and pulses, rice, vegetables
etc., can be readily cooked.
The time taken for cooking depends upon the solar radiation and varies from half an hour two and a half
hours.
A single class reflector (mirror) whose inclination can be varied is usually attached to the box type cooker.
The reflector helps in achieving enclosure temperatures which are higher by about 15 – 20 ˚C. As a result,
cooking time is reduced.
SOLAR DRYING
One of the traditional uses of solar energy has been drying of agricultural products.
The drying process removes moisture and helps in the preservation of the product.
A cabinet type solar dryer consists of an enclosure with a transparent cover.
The material to be dried is placed on perforated drying trays.
Solar radiation entering the enclosure is absorbed in the product itself and the surrounding
internal surfaces of the enclosure.
As a result, moisture is removed from the product and the air inside is heated.
Suitable openings at the bottom and the top ensure a natural circulation.
Temperatures ranging from 50 - 80 ̊C are usually attained and drying time ranges from 2 – 4
days. Products dried are: dates, apricots, chillies and grapes.
When the temperature of the product needs to be controlled or when the solar radiation
falling on the product is not adequate, indirect gain forced circulation dryer is used.
Here, the air is heated separately in an array of solar air heaters and then ducted to the
chamber in which the product to be dried is stored.
Suitable for food grains, tea, spices, leather and ceramics.
SOLAR POND
A solar pond is a body of water that collects and stores solar energy. Solar energy will warm
a body of water (that is exposed to the sun), but the water loses its heat unless some method is
used to trap it. Water warmed by the sun expands and rises as it becomes less dense. Once it
reaches the surface, the water loses its heat to the airthrough convection, or evaporates, taking
heat with it. The colder water, which is heavier, moves down to replace the warm water,
creating a natural convective circulation that mixes the water and dissipates the heat. The
design of solar ponds reduces either convection or evaporation in order to store the heat
collected by the pond. They can operate in almost any climate.
A solar pond can store solar heat much more efficiently than a body of water of the same size
because the salinity gradient prevents convection currents. Solar radiation entering the pond
penetrates through to the lower layer, which contains concentrated salt solution. The
temperature in this layer rises since the heat it absorbs from the sunlight is unable to move
upwards to the surface by convection. Solar heat is thus stored in the lower layer of the pond.
WORKING PRINCIPLE
The solar pond works on a very simple principle. It is well-known that water or air is heated
they become lighter and rise upward. Similarly, in an ordinary pond, the sun‟s rays heat the
water and the heated water from within the pond rises and reaches the top but loses the heat
into the atmosphere. The net result is that the pond water remains at the atmospheric
temperature. The solar pond restricts this tendency by dissolving salt in the bottom layer
ofthe pond making it too heavy to rise . You can see a shematic view of a solar pond in
Figure
A solar pond is an artificially constructed water pond in which significant temperature rises
are caused in the lower regions by preventing the occurrence of convection currents. The
more specific terms salt-gradient solar pond or non-convecting solar pond are also used. The
solar pond, which is actually a large area solar collector is a simple technology that uses
water- a pond between one to four metres deep as a working material for three main functions
• Collection of radiant energy and its conversion into heat (upto 95° C)
• Storage of heat and transport of thermal energy out of the system
The solar pond possesses a thermal storage capacity spanning the seasons. The
surface area of the pond affects the amount of solar energy it can collect. The bottom
of the pond is generally lined with a durable plastic liner made from material such as
black polythene and hypalon reinforced with nylon mesh. This dark surface at the
bottom of the pond increases the absorption of solar radiation. Salts like magnesium
chloride, sodium chloride or sodium nitrate are dissolved in the water, the
concentration being densest at the bottom (20% to 30%) and gradually decreasing to
almost zero at the top. Typically, a salt gradient solar pond consists of three zones.
• An upper convective zone of clear fresh water that acts as solar collector/receiver and
which is relatively the most shallow in depth and is generally close to ambient
temperature,
• A gradient which serves as the non-convective zone which is much thicker and
occupies more than half the depth of the pond. Salt concentration and temperature
increase with depth,
A lower convective zone with the densest salt concentration, serving as the heat
storage zone. Almost as thick as the middle non-convective zone, salt concentration
and temperatures are nearly constant in this zone,
When solar radiation strikes the pond, most of it is absorbed by the surface at the
bottom of the pond. The temperature of the dense salt layer therefore increases. If the
pond contained no salt, the bottom layer would be less dense than the top layer as the
heated water expands. The less dense layer would then rise up and the layers would
mix. But the salt density difference keeps the „layers‟ of the solar pond separate. The
denser salt water at the bottom prevents the heat being transferred to the top layer of
fresh water by natural convection, due to which the temperature of the lower layer
may rise to as much as 95°C.
SOLAR DESALINATION
These are separation processes that rely on a technique or technology for
transforming a mixture of substances into two or more distinct components. The purpose of
this type of process is to purify the saline water of its impurities.
The principle of a separation process is to use a difference of properties between the
interest compound and the remaining mixture. When the difference property will be greater,
the separation is easy. So the choice of the separation process starts with a good knowledge
of the mixture composition and properties of different components. The desalination
processes are divided into two main categories: on the one hand, the distillation process
(which requires a phase change, evaporation / condensation) and on the other hand the
membrane processes (filtration).
The most current techniques of desalination are thermal distillation - for the treatment
of great volumes of water (55 000 m3/jour) – and the membranes technology: electrodialysis
and reverse osmosis. The ability of treatment with membrane technology can be adapted
according to the intended use (the great plants have a capacity of more than 5000 m3/day,
the averages plant between 500 and 5000 m3/day, while that small installations have a
maximum capacity of 500 m3/day).
It is noticed that these processes use thermal energy and / or electrical energy and
consequently are consumer‟s energy and pollutants. The energy, conventional methods
commonly used, can be of solar origin either a partial or total depending on production
capacity and in this way we minimize significantly the consumption of energy while
protecting the environment. Future research in this area is oriented toward the maximum
utilization of solar energy, which is free and clean, or through technological innovation
and/or improvements on conventional methods.
For their operation, the distillation processes require for much of the thermal energy
for heating salt water. Furthermore, this thermal energy must be supplied at a relatively low
temperature, between 60 and 120 ° C. Heat can be provided in the case of the use of solar
energy by solar flat plate or concentrator collector according to working conditions.
The processes most commonly used and which are likely to be coupled to a source of solar
energy are:
-The direct solar greenhouse distillation is a properly solar process.
-The conventional distillation processes such as multi-stage flash, multi-effects, vapor
compression
Solar energy is not available at night, making energy storage an important issue in order to
provide the continuous availability of energy. Both wind power and solar power are intermittent
energy sources, meaning that all available output must be taken when it is available and either
stored for when it can be used, or transported, over transmission lines, to where it can be used.
Wind power and solar power tend to be somewhat complementary, as there tends to be more wind
in the winter and more sun in the summer, but on days with no sun and no wind the difference
needs to be made up in some manner. The Institute for Solar Energy Supply Technology of the
University of Kassel pilot-tested a combined power plant linking solar, wind, biogas and
hydrostorage to provide load-following power around the clock, entirely from renewable sources.
Solar energy can be stored at high temperatures using molten salts. Salts are an effective
storage medium because they are low-cost, have a high specific heat capacity and can deliver heat
at temperatures compatible with conventional power systems. The Solar Two used this method of
energy storage, allowing it to store 1.44 TJ in its 68 m³ storage tank, enough to provide full output
for close to 39 hours, with an efficiency of about 99%.
Artificial photosynthesis involves the use of nano technology to store solar electro magnetic
energy in chemical bonds, by splitting water to produce hydrogen fuel or then combining
with carbon dioxide to make bio polymers such as methanol. Many large national and
regional researchprojects on artificial photosynthesis are now trying to develop techniques
integrating improvedlight capture, quantum coherence methods of electron transfer and cheap
catalytic materials thatoperate under a variety of atmospheric conditions.
Solar Heating and Cooling:
Solar thermal energy is appropriate for both heating and cooling. Key applications for solar
technologies are those that require low temperature heat such as domestic water heating,
space heating, pool heating, drying process and certain industrial processes. Solar
applications can also meet cooling needs, with the advantage that the supply (sunny summer
days) and the demand (desire for a cool indoor environment) are well matched. To generate
synergy effects in climates with heating and cooling demand combined systems should be
used.
Solar Heating:
Over 70% of the household‟s energy use goes into space and water heating. Covering a big
part with a solar system leads to energy as well as financial savings. Solar heating is a well
established renewable energy source and applied in numerous projects worldwide. Solar
thermal systems consist of a solar collector, a heat exchanger, storage, a backup system and a
load. This system may serve for both, space heating and tap water heating, known as combi
system.
Passive Solar heating
• A passive solar system uses no external energy, its key element is good design.
• House faces south.
• South facing side has maximum window area (double or triple glazed).
• Roof overhangs to reduce cooling costs.
• Thermal mass inside the house (brick, stones or dark tile).
• Deciduous trees on the south side to cool the house in summer, let light in the winter.
• Insulating drapes (closed at night and in the summer).
• Greenhouse addition.
• Indirect gain systems also such as large concrete walls to transfer heat inside.
Passive Heating
Direct Gain Thermal Storage
W all
Sunspace
Passive Cooling
Shading Vent ilat ion Earth Contact
Active Solar Heating
• Flat plate collectors are usually placed on the roof or ground in the sunlight.
• The sunny side has a glass or plastic cover.
• The inside space is a black absorbing material.
• Air or water is pumped (hence active) through the space to collect the heat.
• Fans or pumps deliver the heat to the house.
Solar Energy Storage Systems
Concrete is a relatively good medium for heat storage in passively heated or cooled houses. It
is also considered for application in intermediate–temperature solar thermal plants.
Consider the thermal energy storage system shown schematically in the below Figure . The
system consist of a large liquid bath of mass m and specific heat C placed in an insulated
vessel. The system also includes a collector to give the collector fluid a heat gain and a room
in which this heat gain is discharged.
Schematic Diagram of the Solar Energy Storage System.
Operation of the system takes place in three steps; charging, storage and removal
processes. At the beginning of the storage process valves A, B, C are opened. Hot fluid from
the collector at temperature Tis enters the system through valve C. This hot collector fluid is
cooled while flowing through the heat exchanger 2 immersed in the bath and leaves at the
bottom of the system at temperature Tes. The heat carrying liquid is then pumped to the
collector with the help of pump 2. The fluid entering the collector takes QH from the sun and
its temperature increases to Tis and the storage cycle is completed. While the hot gas flowing
through the heat exchanger 2, the bath temperature Tb and fluid exit temperature of storage
process Tes approach the hot fluid inlet temperature of storage process Tis. The heating
process is allowed to continue up to the desired storage material (water) temperature. At that
desired moment the valves A, B, C are closed. After the storage period D, E, F are opened, so
the removal process begins. Cold fluid with constant mass flow rate flows through valve F
and gets into the heat exchanger 1 and it receives energy from the liquid bath then leaves the
system through valve D. This heated fluid is then pumped to the radiator to give heat to the
medium (room) and the removal cycle is completed. other controlling unit is located at the
radiator outlet. If the radiator outlet temperature is higher than the tank temperature it stops
the pump 1 automatically.
Phase Change Energy Storage
In latent heat storage the principle is that when heat is applied to the material it changes
its phase from solid to liquid by storing the heat as latent heat of fusion or from liquid to
vapor as latent heat of vaporization. When the stored heat is extracted by the load, the
material will again change its phase from liquid to solid or from vapor to liquid. The
latent heat of transformation from one solid phase into another is small. Solid-vapor and
liquid-vapor transitions have large amounts of heat of transformation, but large changes
in volume make the system complex and impractical. The solid-liquid transformations
involve relatively small changes in volume. Such materials are available in a range of
transition temperatures.
Heat storage through phase change has the advantage of compactness, since the latent
heat of fusion of most materials is very much larger than their enthalpy change for 1 K
or even 0 K.. For example, the ratio of latent heat to specific heat of water is 80, which
means that the energy required to melt one kilogram of ice is 80 times more than that
required to raise the temperature of one kilogram of water one degree Celsius.
Any latent heat thermal energy storage system should have at least the following three
components:a suitable phase change material (PCM) in the desired temperature range, a
containment for the storage substance, and a suitable heat carrying fluid for transferring
the heat effectively from the heat source to the heat storage.
Furthermore, the PCMs undergo solidification and therefore cannot generally be used as heat
transfer media in a solar collector or the load. Many PCMs have poor thermal conductivity
and therefore require large heat exchange area. Others are corrosive and require special
containers. Latent heat storage materials are more expensive than the sensible heat storage
media generally employed, like water and rocks. These increase the system cost.
SOLAR ENERGY STORAGE SYSTEM
Solar Photovoltaic
PV systems are like any other electrical power generating systems, just the equipment used is
different than that used for conventional electromechanical generating systems. However, the principles
of operation and interfacing with other electrical systems remain the same, and are guided by a well-
established body of electrical codes and standards. Although a PV array produces power when exposed
to sunlight, a number of other componentsare required to properly conduct, control, convert, distribute,
and store the energy produced by thearray.
Depending on the functional and operational requirements of the system, the specific
components required may include major components such as a DC-AC power inverter, battery
bank, system and battery controller, auxiliary energy sources and sometimes the specified
electrical load(appliances). In addition, an assortment of balance of system (BOS) hardware,
including wiring,overcurrent, surge protection and disconnect devices, and other power processing
equipment. Figure show a basic diagram of a photovoltaic system and the relationship of individual
components.
Major photovoltaic system components.
Batteries are often used in PV systems for the purpose of storing energy produced by the PV
array during the day, and to supply it to electrical loads as needed (during the night and periods of
cloudy weather). Other reasons batteries are used in PV systems are to operate the PV array near its
maximum power point, to power electrical loads at stable voltages, and to supply surge currents
to electrical loads and inverters. In most cases, a battery charge controller is used in these systems
to protect the battery from overcharge and over discharge.
UNIT-V
SOLAR PHOTOVOLTAICS
Photovoltaic Systems
A photovoltaic (PV) system is able to supply electric energy to a given load by directly
converting solar energy through the photovoltaic effect. The system structure is very flexible. PV
modules are the main building blocks; these can be arranged into arrays to increase electric energy
production. Normally additional equipment is necessary in order to transform energy into a useful
form or store energy for future use. The resulting system will therefore be determined by the
energy needs (or loads) in a particular application.
PV systems are like any other electrical power generating systems, just the equipment used is
different than that used for conventional electromechanical generating systems. However, the
principles of operation and interfacing with other electrical systems remain the same, and are
guided by a well-established body of electrical codes and standards. Although a PV array produces
power when exposed to sunlight, a number of other components are required to properly conduct,
control, convert, distribute, and store the energy produced by the array.
Depending on the functional and operational requirements of the system, the specific
components required may include major components such as a DC-AC power inverter,
battery
bank, system and battery controller, auxiliary energy sources and sometimes the specified
electrical load(appliances). In addition, an assortment of balance of system (BOS) hardware,
including wiring,overcurrent, surge protection and disconnect devices, and other power
processing equipment. Figure show a basic diagram of a photovoltaic system and the
relationship of individual components.
Major photovoltaic system components.
Batteries are often used in PV systems for the purpose of storing energy produced by the PV
array during the day, and to supply it to electrical loads as needed (during the night and
periods of cloudy weather). Other reasons batteries are used in PV systems are to operate the
PV array near its maximum power point, to power electrical loads at stable voltages, and
to supply surge currents to electrical loads and inverters. In most cases, a battery charge
controller is used in these systems to protect the battery from overcharge and over discharge.
Off-grid PV systems have traditionally used rechargeable batteries to store excesselectricity.
With grid-tied systems, excess electricity can be sent to the transmission grid. Net metering
programs give these systems a credit for the electricity they deliver to the grid. This credit
offsets electricity provided from the grid when the system cannot meet demand, effectively
using the grid as a storage mechanism. Credits are normally rolled over month to month and any
remaining surplus settled annually.Pumped-storage hydroelectricity stores energy in the form of
water pumped when surplus electricity is available, from a lower elevation reservoir to a higher
elevation one. The energy is recovered when demand is high by releasing the water: the pump
becomes a turbine, and the motor a hydroelectric power generator.
PV systems can be broadly classified in two major groups:
1) Stand-Alone: These systems are isolated from the electric distribution grid.
Figure 5.1 describes the most common system configuration. The system
described in Figure 5.1 is actually one of the most complex; and includes all the
elements necessary to serve AC appliances in a common household or
commercial application. An additional generator (e.g., bio-diesel or wind) could
be considered to enhance the reliability but it is not necessary. The number of
components in the system will depend on the type of load that is being served.
The inverter could be eliminated or replaced by a DC to DC converter if only
DC loads are to be fed by the PV modules. It is also possible to directly couple
a PV array to a DC load when alternative storage methods are used or when
operating schedules are not of importance. A good example may be water
pumping applications were a PV module is directly coupled to a DC pump,
water is stored in a tank through the day whenever energy is available.
Figure 5.1 Stand-Alone Photovoltaic System
o Grid-Tied: These systems are directly coupled to the electric distribution
network and do not require battery storage. Figure 5.2 describes the
basic system configuration. Electric energy is either sold or bought from
the local electric utility depending on the local energy load patterns and
the solar resource variation during the day, this operation mode requires
an inverter to convert DC currents to AC currents. There are many
benefits that could be obtained from using grid-tied PV systems instead
of the traditional stand-alone schemes.
o Smaller PV arrays can supply the same load reliably.
o Less balance of system components are needed. o Comparable emission reduction potential taking advantage of existing
infrastructure.
o Eliminates the need for energy storage and the costs associated to substituting and recycling batteries for individual clients. Storage can be included if desired to enhance reliability for the client.
o Takes advantage of the existing electrical infrastructure. o Efficient use of available energy. Contributes to the required electrical
grid generation while the client’s demand is below PV output.
Figure 5.2 Grid-Tied Photovoltaic System
Hybrid systems may be possible were battery storage or a generator (or both) can be
combined with a grid connection for additional reliability and scheduling flexibility (at
additional cost). Most of the installed residential, commercial and central scale systems
use pre-fabricated flat plate solar modules, because they are widely available. Most
available reports on PV system costs are therefore related to this kind of technology
and shall be our focus in this chapter. Other specialized technologies are available (e.g.,
concentrating PV systems), but not as commercially available as the traditional PV
module.
Electricity Generation with Solar Cells
The photovoltaic effect is the basic physical process through which a PV cell converts
sunlight into electricity. Sunlight is composed of photons (like energy accumulations),
or particles of solar energy. These photons contain various amounts of energy
corresponding to the different wavelengths of the solar spectrum. When photons hit a
PV cell, they may be reflected or absorbed. Only the absorbed photons generate
electricity. When this happens, the energy of the photon is transferred to an electron in
an atom of the cell (usually silicon atoms). The electron is able to escape from its
normal position associated in the atom to become part of the current in an electrical
circuit.
To produce the electric field within a PV cell, the manufacturers create a junction of
two different semiconductors (types P and N). The most common way of making P or
N type silicon material is adding an element that has an extra electron or has a deficit of
an electron. Silicon is the most common material used in manufacturing process of
photovoltaic cells. Silicon atoms have 14 electrons, where the four electrons in the last
layer are called valence electrons. In a crystal solid, each silicon atom normally shares
one of its four valence electrons in a covalent junction with another silicon atom. The
silicon crystal molecule is formed of 5 silicon atoms in a covalent junction.
The process of doping introduces an atom of another element into the silicon crystal to
alter its electrical properties. The element used for doping has three or five valence
electrons. Usually Phosphorus is used to make the N type (Phosphorus has 5 valence
electrons) and Boron the P type (Boron has 3 valence electrons). In a polycrystalline
thin-film cell the top layer is made of a different semiconductor material than the
bottom semiconductor layer .
Besides the positively charged protons and the uncharged neutrons inside the nucleus an atom is composed of the negatively charged electrons that assume discrete energy levels (such as "shells" or "orbitales") around the nucleus. There is a limited number of electrons that can occupy a certain energy level; according to the so-called Pauli exclusion principle any possible energy level
may only be occupied by a maximum of two electrons. These two electrons are only allowed if they again differ from each other by their "spin" (i.e. self angular momentum).
Conductors: (metals and their alloys) two different conditions might occur:
The most energy-rich band (i.e. conduction band) occupied by electrons is not entirely occupied.The most energy-rich band fully occupied with electrons (i.e. valence band) and the conduction band located on top overlap, so that also a partly
covered band (conduction band) is formed. electrical conductors are characterized by a low specific resistance.With rising temperature, the increasing thermal oscillation of the atomic cores impedes the movement of the electrons.This is why
the specific resistance of metals increases with a rising temperature.
Insulators:
• (e.g. rubber, ceramics) are characterized by a valence band fully filled with
electrons, a wide energy gap (Eg > 3 eV) and an empty conduction band.
• Hence, insulators possess virtually no freely moving electrons.
• Only at very high temperatures (strong "thermal excitation") are a small number of electrons able to overcome the energy gap.
• Thus, ceramics, for instance, show conductivity only at very high temperatures.
Semiconductors:
(e.g. silicon, germanium, galliumarsenide) are insulators with a relatively narrow energy gap
(0.1 eV < Eg < 3 eV).
Therefore, at low temperatures, a chemically pure semiconductor acts as an insulator.
Only by adding thermal energy, electrons are released from their chemical bond, and lifted to the conduction band.
This is the reason why semiconductors become conductive with increasing temperatures.
This is the other way round compared to metals, where conductivity decreases with rising temperatures.
Regarding specific resistance, semiconductors are in-between conductors and insulators.
Within the transition area between semiconductors and conductors, in case of very narrow energy gaps (0 eV < Eg < 0.1 eV), such elements are also referred to as metalloids or semi-
metals as they may show similar conductivity as metals. However, unlike "real" metals they are characterized by a reduced conductivity with
decreasing temperatures.
Crystalline silicon is such an indirect semiconductor, and silicon cells must thus be relatively thick and/or contain an appropriate light-trapping scheme to generate a prolonged
optical path length.
Amorphous silicon, CdTe or CIS are in contrast direct semiconductors.
Solar cells made of these materials can thus have a thickness clearly below 10 μm, while the thickness of crystalline silicon solar cells typically stretches from 200 to 300 μm.
Thinner crystalline silicon cells are under development, but must be
provided with the discussed optical properties, resulting in increased manufacturing expenditure.
Photo Effect
The term "photo effect" refers to the energy transfer from photons (i.e. quantum of electromagnetic radiation) to electrons contained inside material.
Photon energy is thereby converted into potential and kinetic energy of electrons.
The electron absorbs the entire quantum energy of the photon defined as the product of Planck's quantum and the photon frequency.
PN Junction
• If p- and n-doped materials brought into contact, holes from the p-doped side diffuse into the n-type region and vice versa.
• First a strong concentration gradient is formed at the p-n- junction, consisting of electrons inside the conduction band and holes inside the valence band.
• Due to this concentration, gradient holes from the p-region diffuse into the n-region while electrons diffuse from the n- to the p area.
• Due to the diffusion, the number of majority carriers are reduced on both sides of the p-n-junction.
• The charge attached to the stationary donors or acceptors then creates a negative space charge on the p-side of the transition area and a positive space charge on the n-
side.
As a result of the equilibrated concentration of free charge carriers an electrical field is built up across
the border interface (p-n-junction).
The described process creates a depletion layer in which diffusion flow and reverse current
compensate each other.
The no longer compensated stationary charges of donors and acceptors define a depletion layer whose
width is dependent on the doping concentration
Photovoltaic Effect
If photons, the quantum's of light energy, hit and penetrate into a semiconductor, they can transfer
their energy to an electron from the valance band
• If such a photon is absorbed within the depletion layer, the region’s electrical field directly
separates the created charge carrier pair The electron moves towards the n-region, whereas the
hole moves to the p-region.
• If, during such light absorption, electron-hole-pairs are created outside of the depletion
region within the p- or n region (i.e. outside of the electrical field), they may also reach the space-
charge region by diffusion due to thermal movements (i.e. without the direction being
predetermined by an electrical field).
• At this point the respective minority carriers (i.e. the electrons within the p-region and the
holes in the n-region) are collected by the electrical field of the space-charge region and are
transferred to the opposite side.
• The potential barrier of the depletion layer, in contrast, reflects the respective majority
carriers.
Photovoltaic Cell And Module
• The basic structure of a photovoltaic cell consisting of p-conducting base material and an n-
conducting layer on the topside.
• The entire cell rear side is covered with a metallic contact while the irradiated side is
• equipped with a finger-type contact system to minimize shading losses.
• Also full cover, transparent conductive layers are used.
• To reduce reflection losses the cell surface may additionally be provided with an anti-
reflecting coating.
• A silicon solar cell with such construction usually has a blue color. By the incorporation of
inverse pyramids into the surface reflection losses are further reduced.
• The inclination of the pyramid surfaces is such that photons are reflected onto another
pyramid surface, and thus considerably enhance the possibility of photon penetration into the
crystal.
• Absorption of the solar light by these cells is almost complete, the cells appear black
Solar cell
• Since solar cells are (still) relatively expensive, there is a tendency to concentrate solar
radiation and thus to reduce the required surface of the photovoltaic cells.
• Furthermore, efficiencies of photovoltaic cells tend to increase with increased irradiance – if
cell temperature remains constant.
• For concentrating systems, more expensive but more efficient solar cell technologies may be
applied cost-efficiently.
For instance, mirror and lens systems are used to concentrate solar radiation.
• But under these circumstances tracking systems are additionally needed, helping to enhance
the energy yield per unit surface.
• Such concentrating systems are most suitable for direct radiation (only direct radiation can
be focused) and thus for regions throughout the world where the solar radiation is determined by
direct irradiance (like in deserts).
Intrinsic conductivity:
Semiconductors are conductive beyond a certain temperature level as valence electrons are released from their chemical bonds with increasing temperatures and thus reach the conduction band (intrinsic conductivity).
They become conduction electrons that are able to move freely through the crystal
lattice (i.e. electron conduction).
On the other hand, also the resulting hole inside the valence band can move through the semiconductor material, since a neighboring electron can advance to the hole.
Holes thus contribute equally to conductivity (hole conduction).
Since every free electron creates a hole within undisturbed pure semiconductor crystals both types of charge carriers equally exists.
Energy gap model
• Intrinsic conductivity is counteracted by recombination, namely the recombination of a free electron and a positive hole.
• Despite this recombination the number of holes and free electrons remains equal since at a certain temperature level always the same number of electron-hole-pairs are
formed as recombine.
For every temperature, there thus exists an equilibrium state with a certain number of free holes and free electrons.
• The number of free electron-hole-pairs increases with rising temperature.
Solar cells for concentrating photovoltaic systems:
• Solar cells of concentrating photovoltaic systems are illuminated up to 500 times more at standard test conditions (STC) compared to fixed mounted cells.
• However, at higher radiation concentrations the serial resistance constitutes a major problem due to the high currents.
• This is why concentrator cells must be especially highly doped and be provided with low-loss contacts
• Terrestrial concentrating photovoltaic systems are almost exclusively provided with silicon-based solar cells, whose structure is similar to that of the highly efficient silicon
solar cells mentioned above.
• On a laboratory scale, they reach electrical efficiencies of up to 29 % at 140- fold concentration of the radiation.
For such concentrator systems it is of particular importance to avoid high temperatures, which will cause power losses.
Further more it has to be taken into consideration that high concentration factors, in the range of several 100's, do need a two axis tracking system and only direct radiation can be used.
Polycrystalline Si Monocrystalline Si
*Thin film solar cells made of crystalline silicon (Different process)
Solar Module
Photovoltaic Systems Total Costs Overview
The PV industry is rapidly maturing because of worldwide environmental concerns and
its energy production potential due to the widely available free solar resource. The
industry is in a race to achieve grid parity (PV energy costs equal to conventional
utility costs) and increase competitiveness in the energy markets. PV system installed
costsrange from 4,600 to 19,500 $/kW (typically the size of the PV array is used to
determine the kW or W rating of the system when complete system costs are
considered). Common figures are 8,000 $/kW for grid-tied systems, and 14,000 $/kW
for stand-alone systems. Energy production costs are typically estimated above
0.18
$/kWh in the United States, yet these energy costs are highly dependent on the
available solar resource at the location under study and cannot be used as a general
reference. Table 5.1 summarizes some of these factors.
Table 5.1 Summary of Factors Affecting PV System Costs and Feasibility
Factors Facts
Grid connection
Grid-connected systems do not need batteries which reduces
considerably initial capital costs and energy costs.
For a comparable load, grid-tied systems use smaller PV
arrays than stand-alone systems.
Grid-Tied systems are estimated to cost ~$4,800/kW less
than stand-alone systems including inverters and batteries
according to the study in systems built in the US between
1997-2000.
Distance to nearest Stand-alone systems tend to become feasible In
utility grid locations which are far from electrical distribution networks.
Grid extensions can cost thousands of dollars per mile of
transmission line.
Solar resource
Solar resource will not affect capital costs but the
availability of solar energy does affect the cost of producing
energy, hence the payback period for the investment.
According to location is considered the second largest
factor affecting PV system cost performance.
Location can have influence on shading patterns, soiling,
operating temperature and solar resource variations.
BOS (tracking)
Balance of system components is estimated to represent 30-
50% of the total costs of a PV System.
Most cost reductions for PV systems over the last decade
are in BOS components including inverters.
Local safety codes or regulations can require additional
balance of system costs for the installation.
Type of installation ,
Mounting, size and Space
When flat roofs are considered, 10o tilt uses 30% more roof
area when flat roofs are considered Commercial and
industrial clients prefer horizontal installation to maximize
flat roof utilization and to lower mounting expenses.
Retrofit installations tend to be more expensive than those
planned for new buildings. According to : Large residential projects are ~$1.2/Wac less
expensive.
Affordable Housing projects are ~$1.9/Wac less
expensive. Custom New House ~$0.18/Wac more
expensive.
Large Scale systems tend to be less expensive on a per watt
basis. Due to the volume or the purchases, developers take
advantage of wholesale prices or discounts. This is also true
for large residential projects as discussed above.
Due to capital cost restrictions, stand-alone systems tend to
be smaller or used for smaller loads.
Grid-tied systems tend to be larger because they provide
lower capital costs and energy costs for larger loads.
Typically larger systems tend to have lower cost per
kW. According to costs diminish ~$40 for every additional
kW.
Module technology
Modules account for 40-50% of total system costs.
Module efficiency determines the total area needed to install
the system. Less area per watt is desired to maximize roof or land use.
PV modules that require less material, energy and time to
develop have lower costs (details below).
PV production
Supply and demand laws have been slowing the cost of PV
modules in the last years. Market shortage of PV modules
has been particularly driven by high demand and silicon
supply shortage.
US production of both silicon and PV modules is constantly
increasing to satisfy the demand.
Many research efforts today seek to reduce the quantity of
materials used per module, one example is thin-film cell
technology.
A doubling in PV production results in ~20% module price
reduction .
Time and Learning
Curve
According to next year cost reduction for systems built in
the US between the years 1997 and 2000 is ~ $600/kW.
According to a 7.3% annual decline has been observed on
small scale system costs since 1998. Large scale systems
showed lower reductions, yet these tend to be less expensive
for each watt of capacity.
Lower component costs are complemented by the acquired
knowledge by system designers and installers who can
perform their jobs more efficiently as they
gain experience, reducing overall costs as well.
O&M
Most PV systems do not have notable O&M costs especially
grid-tied systems.
The study in suggests $11/kW/yr. for small residential and
commercial systems and $27/kW/yr.
According to O&M costs may range between 0.4 to 9.5 cents/kWh although most tend to the lower limit.
Most small scale grid-tied systems do not have moving parts
and therefore maintenance is minimal.
Large-scale systems may use tracking systems and therefore
may require more work.
Battery assisted systems may require acid refills when valve
regulated batteries are not used.
Some arrays will require regular cleaning. This could
represent additional costs especially for large scale systems.
Tree branch trimming may be also considered O&M costs
were applicable.
Batteries, inverters and charge controllers will probably
require at least one replacement during project lifetime, it is
therefore important to consider equipment lifetime and
replacement cost as part of
O&M costs during a projects lifetime. Insurance and
inspection should also be considered.
Energy Use and Cost
System size depends mostly on energy use, solar resource
and component efficiency.
Reducing energy consumption greatly reduces the initial
capital cost investment necessary.
The average energy use for the US is ~10W/ft2.
Average residential energy use in Puerto Rico is
~800kWh/month.
PV systems can be cost competitive in locations with high
energy prices and Net metering programs. The assumption
that PV is expensive is therefore relative to the solar
resource and utility energy prices in a
location.
Indirect benefits (home
value, GHG reduction,
etc.)
Home appraisal is estimated at ~$20 for every $1 reduction
in annual utility bills .
Customers would pay 10% more for a solar equipped residence .
Emissions reductions provide a wide range of economical,
environmental and health benefits. These are difficult to
quantify, yet they cannot be ignored.
Available grants or
Incentive Programs
PV technology is considered very expensive in most
applications; therefore several strategies have been
implemented to jumpstart the widespread use of the
technology. Some of these are:
Tax Deductions
Renewable Energy Credits
Emissions Reduction Credits
Net Metering Programs
Accelerated Depreciation
Grants
Not all have positive effects; therefore incentive
programs should be carefully tailored.
Financing and
economic variables
Debt term, debt ratio, interest rate and project life have
market effect on payback time and energy costs.
Small systems (residential or commercial) can be financed
at 7-8.5% interest rates, these numbers coincide with local
financing institutions.
Larger systems can be financed at lower rates.
Project specific financial parameters are not the only factors
having effect on PV system economic performance. The
economic performance is also affected by external
parameters like inflation and energy escalation rates.
Energy costs in Puerto Rico are currently between
$0.21 and $0.25, and rising due to the heavy dependence on
petroleum derived fuels (June 2008).
In Puerto Rico inflation is 8%, energy cost escalation rate is
14% .
Utilities generally use MARR values between 3 and 18%.
The 6 to 11% range is most common .
According to average MARR values for private investment (big money) or corporations are:
40% for high risk investments (new products, new
business, acquisitions, joint ventures).
25% for medium risk investments (capacity increase
to supply forecasted sales).
15% for low risk investments (Cost improvement,
make v.s. buy, capacity increase to meet existing
orders).
MARR values for individuals are not commonly
available and are difficult to calculate.
20 year debt terms are common for utilities.
12 year debt terms are common for developers.
Residential systems can be financed with debt terms in the
range of 5 to 15 years. Is systems are financed as part of
residential mortages, debt terms would tend to the upper
limit. Personal loans tens to the lower limits.
5 year MACRS depreciation methods are common in many
incentive programs.
Photovoltaic Energy Equipment: General Characteristics and Costs
Cost information on individual components and labor affecting the overall cost of grid- tied PV
systems is compiled below along with a brief description of each item. The data for individual
components represents the estimated average unit cost for an individual unit, not considering
bulk or wholesale special prices. The information found agrees with the total costs information
compiled in the previous section.
1) Photovoltaic (PV) Modules: The basic building block of a photovoltaic module is the
photovoltaic cell; these convert solar energy into electricity. The power output will depend
on the amount of energy incident on the surface of the cell and the operating temperature of
the photovoltaic cell. The power output of a single cell can supply small loads like
calculators or watches, but in order to be useful for high energy demand projects these cells
must be arranged in series and parallel connections. A photovoltaic module is an array of
photovoltaic cells pre-arranged in a single mounting mold. The type of module is therefore
determined by the cells that compose the module itself. There are three dominating cell
technologies:
Monocrystalline: As the name implies, these are cells that are grown from
a single crystal. The production methods are difficult and expensive.
These tend to be more efficient (more power in less area) and more
expensive.
Multicrystalline: The production process allows multiple crystalline
structures to develop within the cell. It is easier to implement in a
production line. It is relatively cheaper than mono- crystalline at the
expense of lower efficiency.
Thin-film: Uses less silicon to develop the cell (hence the name thin film)
allowing for cheaper production costs (silicon is in high demand). It tends
to be less expensive but has also lower efficiency.
The overall efficiency of the module will depend on the cell efficiency and placement
within the module, and on the laminating materials used. The standard testing condition
(STC), defined as a total irradiance of 1000W/m2 and an ambient temperature of 25oC, is
used to define module ratings. Typical module efficiencies range between 11% and 17%
for crystalline technologies at STC; most of the commercially available modules are in
the lower bound of this range. Thin-film module efficiencies range between 6% and 12%
. Since 2003 total PV production grew in average 50%, whereas the thin film segment
grew almost 80% and reached 196 MW or 8% of total PV production in 2006. About
90% of the current production uses wafer-based crystalline silicon technology. The main
advantage of this technology was that complete
production lines could be bought, installed and manufactured within a relatively short
time. This predictable production start-up scenario constitutes a low-risk placement with
high expectations for return on investments.The technology is receiving much benefit
from research that strives to make existing technologies cheaper and more accessible. The
Energy Information Administration (EIA) reports that 26 companies were expected to
introduce new photovoltaic products in the market in the year 2007. Recent years have
presented new alternatives to the way solar modules are built and implemented.
Examples of creativity include shingles and windows that use photovoltaic cells as part of
their design. Architects and engineers have developed ways to use PV modules in
building facades substituting them for regular building materials, hence reducing the net
cost of the PV generated energy. The approach is known as building integrated
photovoltaic (BIPV) architecture.
2) Inverters: Inverters are used to transform DC current into AC currents. In the photovoltaic
industry, inverters can be classified into two broad categories:
Stand-Alone Inverters- These inverters are meant to operate isolated from
the electrical distribution network and require batteries for proper
operation. The batteries provide a constant voltage source at the DC input
of the inverter. Inverters can be classified briefly as:
Square Wave Inverters
Modified Sine Wave Inverters
Sine wave inverters (quasi-sine wave).
Voltage and current waveforms produced by inverters are never perfect
sinusoids (even for sine wave inverters); therefore some harmonic currents
are expected during normal system operation. Total harmonic distortion
(THD) is a measure of the harmonic content in current and voltage
waveform. The type of inverter used will depend on the load that it will
serve. Resistive loads could tolerate square wave inverters which are
cheaper and easier to develop. Motors and sensitive electronics will need
inverters that are able to produce almost perfect sinusoidal voltage and
current waveforms in order to operate correctly. These tend to be more
expensive and difficult to design. The designer should choose inverters
according to load types and power requirements. Modern stand-alone
inverters have software applications embedded that monitor and control
equipment operation.
Grid-Tied Inverters- These inverters operate coupled to the electric
distribution network and therefore must be able to produce almost perfect
sinusoidal voltages and currents. The operating requirements for these
types of inverters are in most cases determined by the local utilities, yet
most utilities rely on existing standards to determine feasible technologies.
The most referenced standards in the United States are the IEEE1547 and
the UL 1741. These standards include the minimum requirements that
manufacturers should include into their inverter designs in order to prevent
adverse effects in the distribution grid [20]-[24]. Normally, embedded
software applications monitor and control equipment operation to comply
with standard requirements. There are two main categories of grid-tied
inverters. Line-commutated inverters
derive their switching signals directly from the grid line currents. The low
switching frequencies produce harmonic currents that need to be filtered
out. In the case of small single-phase inverters the bulky and expensive
filtering networks are not practical. In the case of large three phase
inverters, multiple units could be connected through a multi-phase
isolation transformer at the utility output, filtering any unwanted currents .
Self-commutated inverters derive their switching frequencies from internal
control units as they monitor grid conditions, in particular frequency and
voltage. High switching frequencies (3 – 20 kHz) are used and therefore
lower current harmonic content is possible without the need of using large
filtering networks. Self-commutated inverters can be either voltage source
inverters or current source inverters. PV modules behave like voltage
sources; therefore our interest will be in voltage source type inverters.
Voltage source type inverters can yet again be subdivided into current
control and voltage control types. In applications where there is no grid
reference, voltage control schemes are used and the inverter behaves as a
voltage source. Where a grid connection is used the current control
scheme is used and the inverter behaves as a current source. These
inverters use the utility voltage as reference to provide the current
available from the PV, and are not able to operate as an island. The
advantages of current control voltage source inverters are:
Power Factor (PF) ~ 1 (employing a simple control scheme).
Transient Current Suppression: The fault current is limited in the
range of 100% to 200% rms rated current. The fault contributions
of these inverters are limited by their control and protection
system. The fast switching frequencies these inverters use, allow
them to detect large currents that may exceed their semiconductor
ratings and stop operation within 0.5 cycles .
Some stand-alone inverters can also be operated as grid-tied inverters or in combination
with other renewable energy sources as part of hybrid power systems. Modern inverters
can achieve efficiencies higher than 95% (especially grid-tied inverters) and are
warranted for 5 to 10 years in most cases. Most inverters have efficiencies above 85%.
3) Batteries: These are most commonly used to store energy in stand-alone applications for use
at times when no irradiance is available (e.g. night, rainy day). Batteries are also used for a
diverse number of applications including stand-by power and utility interactive schemes. PV
batteries require tolerance to deep discharges and irregular charging patterns. Some
applications may require the batteries to remain at a random state of charge for a prolonged
time. The most common technology used in PV systems is the lead-acid battery. These
batteries are available in two major categories:
Flooded (Vented)- This is the regular battery technology most people are
used to. It tends to be the cheapest option when only initial costs are of
interest. In this battery, overcharge results in the conversion of water into
hydrogen and oxygen gases. The gases are released into the atmosphere;
hence the batteries require that the water is replaced adding a maintenance
cost to the system.
Valve Regulated- The chemical characteristics of these batteries allow for
maintenance free operation because the oxygen is allowed to recombine
with the hydrogen within the battery. The recombination has a maximum
rate which depends on the charging current. If excess pressure builds up, it
is vented through valves to the atmosphere, proper charge control can limit
this effect. These batteries tend to allow deeper discharge cycles resulting
in smaller battery banks and are expected to have longer life times. There
are two main technologies available: Absorbed glass mat (AGM) and Gel.
Another advantage of these sealed batteries is that most are spill
proof.Nickel-Cadmium batteries can also be used in PV applications,
especially where extreme temperatures are expected that could lower the
battery life of lead-acid batteries. Some batteries of this technology allow
discharges of 90% or more of rated capacity and tolerate prolonged
periods at sub-optimal state of charge without damage or memory effect.
Nickel-Cadmium batteries are 3 to 4 times more expensive per stored kWh
and are highly difficult to dispose off due to their toxic potential. Battery
technology is relatively old, and is often regarded as the weakest link in
photovoltaic systems. Improper care of the batteries can seriously affect
battery lifetime.
4) Balance of System Components (BOS) and Charge Controllers: BOS components typically
constitute 30-50% of total system costs. They are all the additional elements necessary in
order to properly install the PV system. The minimum requirements are regulated in the 2005
NEC (the 2008 version is now available as well) . A comprehensive overview can be found
in BOS components may include:
Conductors, conduits and boxes
Overcurrent Protection (e.g. Fuses and Breakers)
Ground Fault Protection
Mounting Gear (support structure)
Disconnects
Metering Equipment
Maximum Power Point Trackers
Charge Controllers
Battery Enclosures
The cost of the support structure could vary considerably depending on whether the system is
to be mounted on the building wall, or roof, or whether it is to be ground mounted. For an
array installed flush into a ceiling, support structure costs are negligible. More complicated
structures may cost ~$200/m2. Tracking system costs are in the $300 to $1,200 per m2. Large
or simple structures are in the lower boundary region of this range. Small complicated
tracking systems are in the upper boundary region of this range.
System installation is in the $900 to $2,500 per kW . Installation costs depend on system
size, location and complexity. Larger systems could require heavy machinery and larger
crews. Land based systems could require terrain preparation and trench digging.
Electrical equipment could cost ~$700/kW for simple or residential systems and
~$1,500/kW for industrial systems . Costs are determined by system complexity and system
size. Stand-alone systems generally have higher costs than grid-connected systems on a per
watt basis.
Charge controllers are part of the electrical equipment costs. These control the current flow
from the PV array to the battery in order to ensure proper charging. These controllers
disconnect the PV array from the battery whenever produced energy exceeds battery storage
capacity or the load whenever charge levels are dangerously low or reach a certain threshold.
It is common for charge controllers to monitor battery voltage, temperature, or a combination
of both to determine depth of discharge. The controllers extend battery life and are a safety
requirement of the National Electrical Code (NEC) for residential and commercial
installations. It is important to select a proper charge controller and controller settings for the
battery type selected for the system. Some controllers can be adjusted to accommodate
different battery types; some are built for specific battery technologies exclusively. Today,
commercially available controllers can achieve efficiencies as high as 95%. Most charge
controllers currently available rely on solid state technology to control current flowing into
the battery bank; still some electromechanical relay versions available. Electromechanical
relays can only perform classic on/off control (therefore little flexibility is possible), this
control strategy can still be rough on the battery. Solid state controllers are more varied or
flexible in terms of control strategies. Some of the possibilities are:
On-off
Constant Voltage
PWM, constant voltage and with current regulation
MPPT
The PV industry is relatively new. The industry has space for small companies which specialize
in specific equipment, or large corporations which have expanded their product range to include
PV related equipment. A list of component manufacturers has been compiled in Table 5.2.
PV Modules
A number of solar cells electrically connected to each other and mounted in a support structure
are called a photovoltaic module. Modules are designed to supply electricity at a certain DC
voltages such as 12, 24 or 48 volts. The current produced is directly dependent on how much
light hits the module. Multiple modules can be wired together to form an array. A larger area of a
module or array will produce more electricity. PV modules are rated on the basis of the power
delivered under Standard Testing Conditions (STC) of 1 kW/m² of sunlight and a PV cell
temperature of 25 degrees Celsius (°C). Their output measured under STC is expressed in terms
of “peak Watt” or Wp nominal capacity ]. A typical crystalline silicon module consists of a series
circuit of 36 cells, encapsulated in a glass and plastic package for protection from the
environment. Although PV modules are warranted for power output for periods from 10-25
years, they can be expected to deliver amounts of energy (voltage and current) for periods of 40
to 50 years . Typical electrical information supplied by the manufacturer includes:
Polarity of output terminals or leads
Maximum series fuse for module protection
Rated open-circuit voltage
Rated operating voltage
Rated operating current
Rated short-circuit current
Rated maximum power
Maximum permissible system voltage
Table 5.3 and Table 5.4 summarize characteristics of various PV cell technologies.
Table 5.3 Photovoltaic categories by semiconductor selection .
Crystalline silicon solar cells
Market Share: 93%
Monocrystalline, produced by slicing
wafers (up to 150 mm diameter and 350
microns thick) from high-purity single
crystal.
Multicrystalline
Thin Film Solar Cells
Market Share: 7%
Amorphous silicon
Pollycristalline materials: Cadmium
Telluride (CdTe), Copper indium
(gallium) Diselenide (CIS or CIGS).
Table 5.4 Advantages and Disadvantages by solar cell technologies .
Cell Type Advantages Disadvantages
Single Crystal Silicon
Well established and
tested technology
Stable
Relatively efficient
Uses a lot of expensive
material
Lots of waste in slicing
wafers
Costly to manufacture
Round cells can’t be spaced in modules
efficiently
Polycrystalline
Silicon
Well established and
tested technology
Stable
Relatively efficient
Less expensive than single
Crystalline Si
Square cells for more
efficient spacing
Uses a lot of expensive
material
Lots of waste in slicing wafers
Fairly costly to
manufacture
Slightly less efficient than
Single Crystalline Si
Ribbon Silicon
Does not require slicing
Less material waste than
single and polycrystalline
Potential for high speed
manufacturing
Relatively efficient
Has not been scaled up to
large-volume production
Complex manufacturing
process
Amorphous Silicon
Very low material use
Potential for highly
automated and very rapid production
Potential for very low cost
Pronounced degradation in
power output
Low efficiency
Inverters
Inverters are electronic solid-state devices used to transform electric energy from DC to AC, as
shown in Figure 5.7. The simplest inverter can be accomplished with a circuit similar to that
shown in Figure 5.8. The ideal switches in the circuit may represent MOSFETs, IGBTs or
bipolar transistors (depending on the power and voltage requirements). If the switches are turned
on and off at the required AC frequency (S1&S3 and S2&S4), a square wave voltage can be
obtained as shown in Figure 5.9. This is a simple control strategy, yet no control of load voltage
is possible and high harmonic currents and voltages are present. High frequency pulse width
modulation techniques are used to diminish harmonic distortion and provide load voltage control.
Harmonic content may cause overheating in motor loads due to higher copper losses as well as
uneven magnetic fields affecting overall operation. Sensitive electronic loads may also display
erratic operation. Today, advanced control schemes and creative topologies allow the creation of
AC with very low harmonic distortion; three phase designs are also possible by incorporating
additional switches.
Figure 5.7 Representation of DC to AC conversion Process
Many industries have found applications for inverters; hence design requirements tend to be
specific to the needs of a particular application. A whole new industry has evolved around the
need of a proper inverter to accommodate the needs of the relatively new solar industry, with
both big and small manufacturers entering the market. PV modules produce DC outputs which
are dependent on the irradiance, temperature and load operation. Stand-alone inverters operating
with energy storage or batteries need a small DC voltage operating range to allow for voltage
differences due to battery state of charge, and surge capacity to allow for safe and uninterrupted
transient event operation. Grid-tied systems do not normally incorporate energy storage; hence
larger DC voltage operating ranges are needed to accommodate both the varying operating
conditions and module configurations. Maximum power point tracking control algorithms are
normally included to take full advantage of the PV module energy production capabilities.
Advanced protection functions are normally also included in order to guarantee safe operation in
parallel with the distribution grid. These are just examples of specific requirements for PV
inverters in their specific applications. The following section shall summarize current PV
inverter characteristics, industry status and trends, especially in the grid-tied market, which is
currently of most public interest. The industry challenges attended include:
1. Reliability
2. Inverter lifetime improvements
3. Higher inverter efficiencies
4. Production cost reduction
5. System and installation cost reduction
6. Unreliable or inadequate components or parts
7. Safety
8. Grid connection issues
9. Optimal circuit topologies, etc.
Grid-Tied inverters operate coupled to the electric distribution network and therefore the
operation requirements are quite different from those of stand-alone inverters. Figure 5.4 shows a
simple block diagram of a grid-connected PV system. Energy Storage is not considered in most
grid-connected applications, hence it is not included in the diagram, but it could be an option
depending on the reliability needs of the owner. In general terms the system can be divided into
the solar panels and the power conditioning equipment, which includes: the maximum power
point tracker, the inverter, the galvanic isolation (optional), and protection and control features.
These components are commonly integrated in the same enclosure or unit as a way to reduce
production and installation costs; hence it has been customary in the PV industry to refer to the
combination of all these elements as the inverter. We shall adopt this practice.
Figure 5.4-Grid-Connected PV System Block Diagram
It is commonly said that grid connected PV systems are as good as their interfaces between the
DC and AC power segments. As an example, the best solar modules in the industry will not be of
great use if the power is not transformed efficiently and safely to useful levels at the load side.
For the utilities it is of no use to allow the integration of DG systems that could degrade the
quality of the electric power in the distribution network. Inverter failure will prevent any useful
energy being produced. Proper inverter systems should include or consider the following:
Maximum Power Point Tracker (MPPT) - Nominal voltage and current conditions
will not be available from the PV array at all times due to constant changes in
solar irradiance. Figure 5.5 displays the I-V curves for a PV module at different
operating characteristics. The MPPT guarantees optimum power is always
obtained from the PV modules at any given operating condition. Different
algorithms have been developed to achieve MPPT control, some achieving more
than 98% of the PV array output capacity. The most popular is the Perturb and
Observe (P&O) algorithm, this algorithm increases or decreases voltage in small
steps and monitors the power output until maximum power point is found. A
summary of available literature is available at .
Figure 5.5- I-V Curves for a PV Module at different operating conditions
Inverter- Inverters have the task of DC/AC conversion. There are two main
categories of grid-tied inverters. Line-commutated inverters derive their switching
signals directly from the grid line currents. The low switching frequencies
produce harmonic currents that need to be filtered out. In the case of small single-
phase inverters the bulky and expensive filtering networks are not practical. In the
case of large three phase inverters, multiple units could be connected through a
multi-phase isolation transformer at the utility output to filter any unwanted
currents; the transformers should be rated to withstand additional heating due to
harmonic current copper losses [20]. Self-commutated inverters derive their
switching frequencies from internal control units as they monitor grid conditions,
in particular frequency and voltage. Self-commutated inverters can be either
voltage source inverters or current source inverters. PV modules behave like
voltage sources; therefore our interest will be in voltage source type inverters.
Voltage source type inverters can yet again be subdivided into current control and
voltage control types. In applications where there is no grid reference, voltage
control schemes are used and the inverter behaves as a voltage source. Where a
grid connection is used the current control scheme is preferred and the inverter
behaves as a current source. Operating the inverter under current control limits the
possibility of active voltage regulation, a high power factor can be obtained with
simpler control circuits (usually the power factor is kept as near to unity as
possible), and transient current suppression is possible when disturbances as
voltage fluctuations occur. Another advantage is that current related power quality
disturbances related to inverter operation, like harmonics, can be controlled with
ease
and independence from voltage quality which then depends entirely on the utility.
Problems caused by unusual utility voltages should be the responsibility of the
utility because they are commonly associated to more complicated problems. It is
important to understand that customer compliance to any standard should be
independent to utility compliance to the same issue; the utility should not assume
that the customer has total responsibility. The disadvantage of operating using
current control is that it cannot operate as an isolated power source. Some
inverters are able to handle both control functions to operate as grid connected
and also provide conversion for storage batteries working as a backup.
According to a survey from the IEA for inverters under 50kW, 19 % of inverters
in the market use voltage control and while 81% use current control. High
switching frequencies (3– 20 kHz) are used in some designs; therefore lower
current harmonic content is possible without the need of using large filtering
networks. The only problem is that higher switching frequencies result in higher
losses reducing the efficiency of the inverter. Designers must find a balance
between efficiency, power quality and size.
Energy Storage
In a PV system the energy produced by PV modules does not always coincide with energy
demanded. A PV array that it is not grid-connected needs to store the energy excess produced by
solar cells. Electrical storage batteries are often employed in Stand Alone PV systems. The
primary functions of a storage battery in a PV system are :
1. Energy Storage and Autonomy: Store electrical energy produced by PV modules and
supply energy as needed for the load.
2. Voltage and Current stabilization: To supply power to electrical loads at stable voltages
and currents.
3. Supply Surge Currents: Supply high peak operating currents to electrical loads or
appliances.
In PV systems, lead-acid batteries are most common due to their wide availability in many sizes,
low cost and well known characteristics. Electrical storage batteries can be divided into Primary
and Secondary Batteries. Table 5.12 shows secondary batteries charge characteristics.
Nickel-Cadmium Charge/discharge characteristics and high cost make them impractical
for most PV systems. Flywheels, hydrogen, and other gas storage also have limited applicability
in residences.
Charge Controllers
The charge controller is a DC to DC converter whose main function is to control the current flow
from the photovoltaic modules array with the purpose of charging batteries. Most of these
devices can maintain the maximum charge of the battery
without overcharging or reaching the minimum design charge. The main functions of a Charge
Controller are:
• Overcharge Protection: The purpose is to prevent the damage in the batteries when they
are charged and the PV array still supplies energy. This protection interrupts or restricts
the current flow from the modules to the batteries and regulates the batteries voltage.
• Over discharge Protection: During periods of excessive use of energy or little solar
irradiation the charge of the batteries could be affected approaching to the point of
minimum discharge. The charge controller disconnects the batteries or stop the current
flow from the batteries to the load (Load Management) to prevent batteries damage.
There are two basic methods for controlling the charging of a battery from a PV module array:
Shunt Controller: Since PV cells are current-limited the basic operation of shunt controller is
short-circuiting the PV modules and arrays. For this reason most shunt controller require a heat
sink to dissipate power. The regulation element of these controllers typically is a power transistor
or MOSFET.
Shunt Interrupting: The shunt interrupting controllers completely disconnect the array current
when the batteries reach the voltage set point. When the batteries voltage decreases, the
controller reconnects the array to resume charging the batteries.
Shunt Linear: When the batteries become nearly fully charged, the controller maintains the
battery near a set point voltage by gradually shunting the array through a semiconductor
regulation element.
Series Interrupting: This is the simpler of series controller (on-off type). The charge controller
constantly monitors the batteries voltage and disconnects the arrays once the batteries reach the
set point. When the batteries voltage drops this controller reconnect the array to charge the
batteries.
Series interrupting, 2 step, Constant Current: The 2 step, constant current controller is similar to
the series interrupting but when the voltage reaches the set point, instead of totally interrupt the
array current, a limited constant current remains flowing to the batteries. This continues either
for a pre-set period of time, or until the voltage drops to the cycle repeats.
Series interrupting, 2 step, Dual Set Point: This type of series charge controller has two distinct
voltage regulation set-points. During the first charge cycle of the day, the controller uses a higher
regulation voltage to maximization of the charge and in the other cycle uses a voltage lower
voltage set-point. The purpose is minimizing the battery gassing and the water loss for flooded
lead-acid type.
Series Linear, Constant Voltage: The linear constant voltage controller maintains the battery
voltage at the voltage regulation set-point. The regulation element acts like a variable resistor
controlled by the battery voltage sensing circuit of the controller, and dissipates the excess of
charge.
Series Interrupting, Pulse Width Modulated: The PWM uses algorithm with a semiconductor
switching element between the array and the batteries. The algorithm switches on-off the charge
of the batteries with a variable frequency and variable duty cycle to maintain the voltage of the
batteries very close to the set-point voltage.
Table 5.14 Controllers Design for Particular Battery types.
Controller Design Type of Batteries
Shunt Interrupting All battery types, but recommended by gel and AGM
lead-acid battery manufactures.
Shunt Linear Sealed VRLA batteries.
Series Interrupting Flooded batteries rather than the sealed VRLA types.
Series Interrupting, 2 step, Constant Current
Series Interrupting, 2 step, Dual Set Point Flooded lead-acid types.
Series Linear, Constant Voltage All battery types.
Series Interrupting, Pulse Width Modulated Preferred use with sealed VRLA.
Apollo Solar GeoSolar Morningstar
Corporation
Trace Engineering
Blue Sky Energy Heliotrope Pulse Energy Systems
Inc
Uhlmann Solarelectronic
GmbH
BZ Products ICP Solar Ses Flexcharge USA Vario
DIREC Lyncom Specialty Concepts
Inc.
Enermaxer Outback Power Sunwize Steca
ETA Engineering Pico Electronics Inc. Sun Selector
Flexcharge Plasmatronics SunAmp Power
BAND GAP THEORY OF SEMICONDUCTORS
In semiconductors and insulators, electrons are confined to a number of bands of energy, and forbidden
from other regions. The term "band gap" refers to the energy difference between the top of the
valence band and the bottom of the conduction band. ... In contrast, a material with a large band gap is an
insulator
In semiconductors and insulators, electrons are confined to a number of bands of energy, and forbidden
from other regions. The term "band gap" refers to the energy difference between the top of the
valence band and the bottom of the conduction band. ... In contrast, a material with a large band gap is an
insulator
In semiconductors and insulators, electrons are confined to a number of bands of energy, and forbidden
from other regions. The term "band gap" refers to the energy difference between the top of the
valence band and the bottom of the conduction band. ... In contrast, a material with a large band gap is an
insulator
So, one good semiconductor material for the future is C (diamond). It has the largest thermal conductivity
and band gap of any of the materials from Table 10.2. Diamond also has the largest electron mobility of
any material from Table 10.2 with a band gap larger than Si.
What is p type and n type?
In a p-type semiconductor, the III group element of the periodic table is added as a doping element,
whereas in n-type the V group element is the doping element. In the n-type semiconductor, electrons are
majority carriers, and holes are minority carriers.
The Fermi Level is the energy level which is occupied by the electron orbital at temperature equals 0 K. ...
There is a gap between the valence and conduction band called the energy gap; the larger the energy gap,
the more energy it is required to transfer the electron from the valence band to the conduction band
Thermo photo voltaic cells
TPV systems are systems that convert thermal energy into electrical energy. These systems are an alternative to
current electrical energy production. Photovoltaic cells convert photon energy from the emitter into electricity
energy
Principle of solar cells
1. Emitter converts heat into radiation
2. This is selectively filtered by optical filter. part of it is transmitted to PV diode and the rest is reflected back to
emitter
3. the PV diode converts the transmitted photons with energies in excess of the diode energy band gap into charge
carriers